Relevant bibliographies by topics / Minimisation problem

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  2. Dissertations / Theses
  3. Books
  4. Book chapters
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Academic literature on the topic 'Minimisation problem'

Author: Grafiati
Published: 12 October 2024

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Journal articles on the topic "Minimisation problem"

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Huy, N. Q., V. Jeyakumar, and G. M. Lee. "Sufficient global optimality conditions for multi-extremal smooth minimisation problems with bounds and linear matrix inequality constraints." ANZIAM Journal 47, no. 4 (April 2006): 439–50. http://dx.doi.org/10.1017/s1446181100010063.

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AbstractIn this paper, we present sufficient conditions for global optimality of a general nonconvex smooth minimisation model problem involving linear matrix inequality constraints with bounds on the variables. The linear matrix inequality constraints are also known as “semidefinite” constraints which arise in many applications, especially in control system analysis and design. Due to the presence of nonconvex objective functions such minimisation problems generally have many local minimisers which are not global minimisers. We develop conditions for identifying global minimisers of the model problem by first constructing a (weighted sum of squares) quadratic underestimator for the twice continuously differentiable objective function of the minimisation problem and then by characterising global minimisers of the easily tractable underestimator over the same feasible region of the original problem. We apply the results to obtain global optimality conditions for optinusation problems with discrete constraints.
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Katzourakis, Nikos. "A minimisation problem in L∞ with PDE and unilateral constraints." ESAIM: Control, Optimisation and Calculus of Variations 26 (2020): 60. http://dx.doi.org/10.1051/cocv/2019034.

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We study the minimisation of a cost functional which measures the misfit on the boundary of a domain between a component of the solution to a certain parametric elliptic PDE system and a prediction of the values of this solution. We pose this problem as a PDE-constrained minimisation problem for a supremal cost functional in L∞, where except for the PDE constraint there is also a unilateral constraint on the parameter. We utilise approximation by PDE-constrained minimisation problems in Lp as p →∞ and the generalised Kuhn-Tucker theory to derive the relevant variational inequalities in Lp and L∞. These results are motivated by the mathematical modelling of the novel bio-medical imaging method of Fluorescent Optical Tomography.
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Hawes, Matthew, and Wei Liu. "Design of Fixed Beamformers Based on Vector-Sensor Arrays." International Journal of Antennas and Propagation 2015 (2015): 1–9. http://dx.doi.org/10.1155/2015/181937.

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Vector-sensor arrays such as those composed of crossed dipole pairs are used as they can account for a signal’s polarisation in addition to the usual direction of arrival information, hence allowing expanded capacity of the system. The problem of designing fixed beamformers based on such an array, with a quaternionic signal model, is considered in this paper. Firstly, we consider the problem of designing the weight coefficients for a fixed set of vector-sensor locations. This can be achieved by minimising the sidelobe levels while keeping a unitary response for the main lobe. The second problem is then how to find a sparse set of sensor locations which can be efficiently used to implement a fixed beamformer. We propose solving this problem by converting the traditionall1norm minimisation associated with compressive sensing into a modifiedl1norm minimisation which simultaneously minimises all four parts of the quaternionic weight coefficients. Further improvements can be made in terms of sparsity by converting the problem into a series of iteratively solved reweighted minimisations, as well as being able to enforce a minimum spacing between active sensor locations. Design examples are provided to verify the effectiveness of the proposed design methods.
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Peldschus, Friedel. "RESEARCH ON THE SENSITIVITY OF MULTI- CRITERION EVALUATION METHODS/SENSIBILITÄTSUNTERSUCHUNGEN ZU METHODEN DER MEHRKRITERIELLEN ENTSCHEIDUNGEN." JOURNAL OF CIVIL ENGINEERING AND MANAGEMENT 7, no. 4 (August 31, 2001): 276–80. http://dx.doi.org/10.3846/13921525.2001.10531736.

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Investigations into the multi-criterion evaluations have been performed for different purposes for more than 30 years. Nevertheless, up to now there are no common rules how to apply multi-criterion methods of evaluation and how to interpret their results. But the solutions of the problem must be found. The investigations are based on the joint programme LEVI developed by the VGTU and the Leipzig HSTEC. In accordance with the programme, for solving the problem a matrix is created in which all solution variants are evaluated by the same criteria. For the transformation of initial data different methods are used. Besides, the problem solution may be oriented to a choice of a variant and the determination of an optimal sequence or to the determination of the rational behaviour balance of two adversely interested groups. The maximisation, minimisation and mixed problems are distinguished. In case of the last mentioned problems the meanings may be unsuitable and expressions about the maximisation or minimisation too strong. When solving the problem of maximisation by different transformation methods, similar curves are obtained and the results are not dispersed heavily. In case of the minimisation, when solving according to different transformations, a considerable deviation of results has been noticed. The investigations also disclosed that solutions may vary depending on the optimisation goal. Dispersion of results in case of minimisation is stronger than in case of maximisation. When analysing different transformations, the vectorial transformation is regarded as “neutral” and there is no sense to include it into comparison. In case of the minimisation problem, linear transformations should be investigated in a more detailed way.
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Khrychev, Dmitry. "Optimal programmed control in energy minimisation problem." E3S Web of Conferences 458 (2023): 01028. http://dx.doi.org/10.1051/e3sconf/202345801028.

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This paper is devoted to the construction of optimal programmed control of the motion of a material point in a medium with a random coefficient of resistance in a homogeneous field of gravity of the Earth. The control objective is to minimise the mathematical expectation of the total mechanical energy of the material point. The problem is solved by two methods proposed by the author in previous works. Both methods assume approximation of the initial stochastic problem by deterministic optimal control problems. In the first case, the transition to approximate deterministic problems is carried out by replacing the parameters representing continuous random variables by discrete-type random variables converging in distribution to the original continuous ones (the method of distribution discretisation). The meaning of such a replacement is that the resulting approximate problem can be considered no longer as a stochastic, but as a deterministic optimal control problem, and can be solved, accordingly, with the help of known standard methods. In the second case, the initial stochastic dynamic system as a result of averaging its equations is replaced first by an infinite system and then, after zeroing all moments of sufficiently high order, by a finite system of equations for mixed moments of the solution and a random parameter (method of moments). The control functions and the optimal values of the quality functional obtained by the two methods were found to be almost identical, and both methods showed good convergence.
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Milovanovic, Milos J., Svetlana S. Raicevic, Dardan O. Klimenta, Nebojsa B. Raicevic, and Bojan D. Perovic. "Determination of Optimal Locations and Parameters of Passive Harmonic Filters in Unbalanced Systems Using the Multiobjective Genetic Algorithm." Elektronika ir Elektrotechnika 30, no. 2 (April 26, 2024): 28–37. http://dx.doi.org/10.5755/j02.eie.36124.

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This paper discusses the problem of optimal placement and sizing of passive harmonic filters to mitigate harmonics in unbalanced distribution systems. The problem is formulated as a nonlinear multiobjective optimisation problem and solved using the multiobjective genetic algorithm. The performance of the proposed algorithm is tested on unbalanced IEEE 13- and 37-bus three-phase systems. The optimal solutions are obtained based on the following objective functions: 1) minimisation of total harmonic distortion in voltage, 2) minimisation of costs of filters, 3) minimisation of voltage unbalances, and 4) a simultaneous minimisation of total harmonic distortion in voltage, costs of filters, and voltage unbalances. Finally, an analysis of the influence of uncertainties of load powers and changes in system frequency and filter parameters on filter efficiency was performed.
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Vaidya, Omkarprasad S., L. Ganapathy, and Sushil Kumar. "A cost minimisation model for system reliability allocation." International Journal of Quality & Reliability Management 36, no. 9 (October 7, 2019): 1620–43. http://dx.doi.org/10.1108/ijqrm-07-2018-0199.

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Purpose The purpose of this paper is to consider a nonlinear problem of minimizing the cost of providing reliable systems. The authors assume that the system consists of several components in series, and for each such component, the cost of the component increases exponentially with its reliability. Design/methodology/approach In order to solve this nonlinear optimization problem, the authors propose two approaches. The first approach is based on the concept of adjusting the reliability of a pair of components to minimize the cost of the system. The authors call this procedure as reliability adjustment routine (RAR). Proofs of optimality and convergence for the proposed model are also provided. The second approach solves the problem by using a Lagrangian multiplier. A procedure is developed to obtain the maximum step size to achieve the desired optimal solution in minimum iterations. Proposed approaches are efficient and give exact solutions. Findings Proposed methods enable a decision maker to allocate reliability to the components in series while minimizing the total cost of the system. The developed procedures are illustrated using a numerical example. Although an exponential relationship between the component cost and reliability is assumed, this can be extended to various other nonlinear distributions. Originality/value This cost optimization problem, subject to system component reliability values, assumes the near practical nonlinear pattern of cost vs reliability. Such problems are complex to solve. The authors provide a unique approach called RAR to solve such convoluted problems. The authors also provide an approach to solve such problems by using a Lagrangian multiplier method. Various proofs have been worked out to substantiate the work.
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Bisira, Hammed, and Abdellah Salhi. "Reshuffle minimisation to improve storage yard operations efficiency." Journal of Algorithms & Computational Technology 15 (January 2021): 174830262199401. http://dx.doi.org/10.1177/1748302621994010.

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There are many ways to measure the efficiency of the storage area management in container terminals. These include minimising the need for container reshuffle especially at the yard level. In this paper, we consider the container reshuffle problem for stacking and retrieving containers. The problem was represented as a binary integer programming model and solved exactly. However, the exact method was not able to return results for large instances. We therefore considered a heuristic approach. A number of heuristics were implemented and compared on static and dynamic reshuffle problems including four new heuristics introduced here. Since heuristics are known to be instance dependent, we proposed a compatibility test to evaluate how well they work when combined to solve a reshuffle problem. Computational results of our methods on realistic instances are reported to be competitive and satisfactory.
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Shang, Zhen, Songzheng Zhao, Yanjun Qian, and Jun Lin. "Exact algorithms for the feedback length minimisation problem." International Journal of Production Research 57, no. 2 (April 24, 2018): 544–59. http://dx.doi.org/10.1080/00207543.2018.1456697.

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Darwish, M. A., Abdulrahman R. Alenezi, and Majid M. Aldaihani. "Per-unit cost minimisation of the newsvendor problem." International Journal of Industrial and Systems Engineering 20, no. 4 (2015): 497. http://dx.doi.org/10.1504/ijise.2015.070186.

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Dissertations / Theses on the topic "Minimisation problem"

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Haben, Stephen A. "Conditioning and preconditioning of the minimisation problem in variational data assimilation." Thesis, University of Reading, 2011. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.541945.

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Coppa, Bertrand. "Sur quelques applications du codage parcimonieux et sa mise en oeuvre." Phd thesis, Université de Grenoble, 2013. http://tel.archives-ouvertes.fr/tel-00934823.

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Le codage parcimonieux permet la reconstruction d'un signal à partir de quelques projections linéaires de celui-ci, sous l'hypothèse que le signal se décompose de manière parcimonieuse, c'est-à-dire avec peu de coefficients, sur un dictionnaire connu. Le codage est simple, et la complexité est déportée sur la reconstruction. Après une explication détaillée du fonctionnement du codage parcimonieux, une présentation de quelques résultats théoriques et quelques simulations pour cerner les performances envisageables, nous nous intéressons à trois problèmes : d'abord, l'étude de conception d'un système permettant le codage d'un signal par une matrice binaire, et des avantages apportés par une telle implémentation. Ensuite, nous nous intéressons à la détermination du dictionnaire de représentation parcimonieuse du signal par des méthodes d'apprentissage. Enfin, nous discutons la possibilité d'effectuer des opérations comme la classification sur le signal sans le reconstruire.
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Wang, Chen. "Variants of Deterministic and Stochastic Nonlinear Optimization Problems." Thesis, Paris 11, 2014. http://www.theses.fr/2014PA112294/document.

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Les problèmes d’optimisation combinatoire sont généralement réputés NP-difficiles, donc il n’y a pas d’algorithmes efficaces pour les résoudre. Afin de trouver des solutions optimales locales ou réalisables, on utilise souvent des heuristiques ou des algorithmes approchés. Les dernières décennies ont vu naitre des méthodes approchées connues sous le nom de métaheuristiques, et qui permettent de trouver une solution approchées. Cette thèse propose de résoudre des problèmes d’optimisation déterministe et stochastique à l’aide de métaheuristiques. Nous avons particulièrement étudié la méthode de voisinage variable connue sous le nom de VNS. Nous avons choisi cet algorithme pour résoudre nos problèmes d’optimisation dans la mesure où VNS permet de trouver des solutions de bonne qualité dans un temps CPU raisonnable. Le premier problème que nous avons étudié dans le cadre de cette thèse est le problème déterministe de largeur de bande de matrices creuses. Il s’agit d’un problème combinatoire difficile, notre VNS a permis de trouver des solutions comparables à celles de la littérature en termes de qualité des résultats mais avec temps de calcul plus compétitif. Nous nous sommes intéressés dans un deuxième temps aux problèmes de réseaux mobiles appelés OFDMA-TDMA. Nous avons étudié le problème d’affectation de ressources dans ce type de réseaux, nous avons proposé deux modèles : Le premier modèle est un modèle déterministe qui permet de maximiser la bande passante du canal pour un réseau OFDMA à débit monodirectionnel appelé Uplink sous contraintes d’énergie utilisée par les utilisateurs et des contraintes d’affectation de porteuses. Pour ce problème, VNS donne de très bons résultats et des bornes de bonne qualité. Le deuxième modèle est un problème stochastique de réseaux OFDMA d’affectation de ressources multi-cellules. Pour résoudre ce problème, on utilise le problème déterministe équivalent auquel on applique la méthode VNS qui dans ce cas permet de trouver des solutions avec un saut de dualité très faible. Les problèmes d’allocation de ressources aussi bien dans les réseaux OFDMA ou dans d’autres domaines peuvent aussi être modélisés sous forme de problèmes d’optimisation bi-niveaux appelés aussi problèmes d’optimisation hiérarchique. Le dernier problème étudié dans le cadre de cette thèse porte sur les problèmes bi-niveaux stochastiques. Pour résoudre le problème lié à l’incertitude dans ce problème, nous avons utilisé l’optimisation robuste plus précisément l’approche appelée « distributionnellement robuste ». Cette approche donne de très bons résultats légèrement conservateurs notamment lorsque le nombre de variables du leader est très supérieur à celui du suiveur. Nos expérimentations ont confirmé l’efficacité de nos méthodes pour l’ensemble des problèmes étudiés
Combinatorial optimization problems are generally NP-hard problems, so they can only rely on heuristic or approximation algorithms to find a local optimum or a feasible solution. During the last decades, more general solving techniques have been proposed, namely metaheuristics which can be applied to many types of combinatorial optimization problems. This PhD thesis proposed to solve the deterministic and stochastic optimization problems with metaheuristics. We studied especially Variable Neighborhood Search (VNS) and choose this algorithm to solve our optimization problems since it is able to find satisfying approximated optimal solutions within a reasonable computation time. Our thesis starts with a relatively simple deterministic combinatorial optimization problem: Bandwidth Minimization Problem. The proposed VNS procedure offers an advantage in terms of CPU time compared to the literature. Then, we focus on resource allocation problems in OFDMA systems, and present two models. The first model aims at maximizing the total bandwidth channel capacity of an uplink OFDMA-TDMA network subject to user power and subcarrier assignment constraints while simultaneously scheduling users in time. For this problem, VNS gives tight bounds. The second model is stochastic resource allocation model for uplink wireless multi-cell OFDMA Networks. After transforming the original model into a deterministic one, the proposed VNS is applied on the deterministic model, and find near optimal solutions. Subsequently, several problems either in OFDMA systems or in many other topics in resource allocation can be modeled as hierarchy problems, e.g., bi-level optimization problems. Thus, we also study stochastic bi-level optimization problems, and use robust optimization framework to deal with uncertainty. The distributionally robust approach can obtain slight conservative solutions when the number of binary variables in the upper level is larger than the number of variables in the lower level. Our numerical results for all the problems studied in this thesis show the performance of our approaches
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Boiger, Wolfgang Josef. "Stabilised finite element approximation for degenerate convex minimisation problems." Doctoral thesis, Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät II, 2013. http://dx.doi.org/10.18452/16790.

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Infimalfolgen nichtkonvexer Variationsprobleme haben aufgrund feiner Oszillationen häufig keinen starken Grenzwert in Sobolevräumen. Diese Oszillationen haben eine physikalische Bedeutung; Finite-Element-Approximationen können sie jedoch im Allgemeinen nicht auflösen. Relaxationsmethoden ersetzen die nichtkonvexe Energie durch ihre (semi)konvexe Hülle. Das entstehende makroskopische Modell ist degeneriert: es ist nicht strikt konvex und hat eventuell mehrere Minimalstellen. Die fehlende Kontrolle der primalen Variablen führt zu Schwierigkeiten bei der a priori und a posteriori Fehlerschätzung, wie der Zuverlässigkeits- Effizienz-Lücke und fehlender starker Konvergenz. Zur Überwindung dieser Schwierigkeiten erweitern Stabilisierungstechniken die relaxierte Energie um einen diskreten, positiv definiten Term. Bartels et al. (IFB, 2004) wenden Stabilisierung auf zweidimensionale Probleme an und beweisen dabei starke Konvergenz der Gradienten. Dieses Ergebnis ist auf glatte Lösungen und quasi-uniforme Netze beschränkt, was adaptive Netzverfeinerungen ausschließt. Die vorliegende Arbeit behandelt einen modifizierten Stabilisierungsterm und beweist auf unstrukturierten Netzen sowohl Konvergenz der Spannungstensoren, als auch starke Konvergenz der Gradienten für glatte Lösungen. Ferner wird der sogenannte Fluss-Fehlerschätzer hergeleitet und dessen Zuverlässigkeit und Effizienz gezeigt. Für Interface-Probleme mit stückweise glatter Lösung wird eine Verfeinerung des Fehlerschätzers entwickelt, die den Fehler der primalen Variablen und ihres Gradienten beschränkt und so starke Konvergenz der Gradienten sichert. Der verfeinerte Fehlerschätzer konvergiert schneller als der Fluss- Fehlerschätzer, und verringert so die Zuverlässigkeits-Effizienz-Lücke. Numerische Experimente mit fünf Benchmark-Tests der Mikrostruktursimulation und Topologieoptimierung ergänzen und bestätigen die theoretischen Ergebnisse.
Infimising sequences of nonconvex variational problems often do not converge strongly in Sobolev spaces due to fine oscillations. These oscillations are physically meaningful; finite element approximations, however, fail to resolve them in general. Relaxation methods replace the nonconvex energy with its (semi)convex hull. This leads to a macroscopic model which is degenerate in the sense that it is not strictly convex and possibly admits multiple minimisers. The lack of control on the primal variable leads to difficulties in the a priori and a posteriori finite element error analysis, such as the reliability-efficiency gap and no strong convergence. To overcome these difficulties, stabilisation techniques add a discrete positive definite term to the relaxed energy. Bartels et al. (IFB, 2004) apply stabilisation to two-dimensional problems and thereby prove strong convergence of gradients. This result is restricted to smooth solutions and quasi-uniform meshes, which prohibit adaptive mesh refinements. This thesis concerns a modified stabilisation term and proves convergence of the stress and, for smooth solutions, strong convergence of gradients, even on unstructured meshes. Furthermore, the thesis derives the so-called flux error estimator and proves its reliability and efficiency. For interface problems with piecewise smooth solutions, a refined version of this error estimator is developed, which provides control of the error of the primal variable and its gradient and thus yields strong convergence of gradients. The refined error estimator converges faster than the flux error estimator and therefore narrows the reliability-efficiency gap. Numerical experiments with five benchmark examples from computational microstructure and topology optimisation complement and confirm the theoretical results.
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Schwinte, Valentin. "Autour de l'équation du plus bas niveau de Landau." Electronic Thesis or Diss., Université de Lorraine, 2024. http://www.theses.fr/2024LORR0078.

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Cette thèse a pour objet l'étude de l'équation du plus bas niveau de Landau, dans plusieurs contextes pertinents en physique et provient des modèles pour les condensats de Bose-Einstein. Nous nous penchons spécifiquement sur trois aspects liés à l'équation. Le premier est l'étude d'une classe de solutions appelées ondes stationnaires, à travers la minimisation d'une fonctionnelle énergie. Nous montrons notamment que la gaussienne est l'unique minimiseur global à symétries près pour un certain paramètre, à l'aide d'algèbre linéaire et bilinéaire. Le deuxième point concerne la conjecture de réseau d'Abrikosov. Nous investiguons l'équation avec ajout de conditions périodiques, et la linéarisons autour des réseaux. Nous aboutirons à la stabilité du réseau hexagonal. Le troisième et dernier aspect porte sur les ondes progressives pour l'équation couplée du plus bas niveau de Landau. Nous classifions de telles solutions ayant un nombre fini de zéros, et en déduisons l'existence de solutions dont les normes de Sobolev croissent
The aim of this thesis is to study the Lowest Landau Level equation, in several contexts relevant to physics and originating from models for Bose-Einstein condensates. In particular, we investigate three aspects of the equation. The first is the study of a class of solutions called stationary waves, through the minimization of an energy functional. In particular, we show that the Gaussian is the only global minimizer up to symmetries for a certain parameter, using linear and bilinear algebra tools. The second point concerns the Abrikosov lattice conjecture. We investigate the equation with the addition of periodic conditions, and linearize it around lattices. This results in the stability of the hexagonal lattice. The third and final aspect concerns progressive waves for the coupled Lowest Landau Level equation. We classify such solutions with a finite number of zeros, and deduce the existence of solutions with growing Sobolev norms
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Cutforth, Claire Louise. "Understanding waste minimisation practices at the individual and household level." Thesis, Cardiff University, 2014. http://orca.cf.ac.uk/69484/.

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Over recent years, the issue of how to manage waste sustainably has intensified for both researchers and policy makers. From a policy perspective, the reason for this intensification can be traced to European legislation and its transposition into UK policy. The Welsh Government in particular has set challenging statutory targets for Local Authorities. Such targets include increases in recycling and composting as well as waste reduction and reuse targets. From a research perspective there has been dissatisfaction with behavioural models and their willingness to explore alternative social science thinking (such as leading approaches to practice). Despite policy interest in sustainable waste practices, there remains little research which focuses specifically on waste minimisation at the individual or household level. What research exists focuses on pro-environmental or recycling behaviour, and tends to focus upon values, intention and behavioural change, rather than on what actual practices occur, and for what reasons. This research focuses on what practices take place in order to access a more complex range of reasons why such practices take place. The methodology adopts a qualitative approach to uncovering practices in a variety of contexts, and discovers a number of key insights which underpin waste minimisation practice. This thesis demonstrates that waste minimisation performances take place, but often do so ‘unwittingly’. Coupled to this, many witting or unwitting waste minimisation actions occur for reasons other than concern for the environment. Furthermore, this research suggests that practices (and their motivations) vary dependent upon the context in which they occur. In general, three key themes were found to be significant in influencing the take up and transfer of practice: cost, convenience, and community. As a waste practitioner, the researcher is able to engage with these themes in order to suggest future directions for waste minimisation policy as well as research.
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Hülsemann, Frank. "A new moving mesh algorithm for the finite element solution of variational problems." Thesis, University of Bristol, 2000. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.310742.

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Gerner, Wadim [Verfasser], Christof [Akademischer Betreuer] Melcher, der Mosel Heiko [Akademischer Betreuer] von, and Daniel [Akademischer Betreuer] Peralta-Salas. "Minimisation problems in ideal magnetohydrodynamics / Wadim Gerner ; Christof Melcher, Heiko von der Mosel, Daniel Peralta-Salas." Aachen : Universitätsbibliothek der RWTH Aachen, 2020. http://d-nb.info/1225880297/34.

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Gryson, Alexis. "Minimisation d'énergie sous contraintes : applications en algèbre linéaire et en contrôle linéaire." Phd thesis, Université des Sciences et Technologie de Lille - Lille I, 2009. http://tel.archives-ouvertes.fr/tel-00424947.

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Le problème de Zolotarev pour des ensembles discrets apparaît pour décrire le taux de convergence de la méthode ADI, dans l'approximation de certaines fonctions matricielles ou encore pour quantifier le taux de décroissance des valeurs singulières de certaines matrices structurées. De plus, la réduction de modèle constitue un enjeu important en théorie du contrôle linéaire, et on peut prédire la qualité de l'approximation d'un système dynamique linéaire continu stationnaire de grande dimension donné grâce à la résolution approchée d'une équation de Sylvester. Après avoir prouvé l'existence d'un minimiseur pour le troisième problème de Zolotarev pour des ensembles discrets, on détermine dans cette thèse le comportement asymptotique faible de ce problème sous certaines hypothèses de régularité. Pour mener cette étude, on considère un problème de minimisation d'énergie sous contraintes pour des mesures signées en théorie du potentiel logarithmique. On discute également la précision de nos résultats asymptotiques pour des ensembles discrets généraux du plan complexe, et une formule intégrale explicite est établie dans le cas particulier de deux sous-ensembles discrets de l'axe réel symétriques par rapport à l'origine. L'impact de nos résultats théoriques pour l'analyse du taux de convergence de la méthode ADI appliquée pour la résolution approchée d'une équation de Lyapounov est estimé à l'aide de plusieurs exemples numériques après avoir exposé l'algorithme nous permettant d'obtenir les paramètres utilisés.
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Haberkorn, Thomas. "Transfert orbital à poussée faible avec minimisation de la consommation : résolution par homotopie différentielle." Toulouse, INPT, 2004. http://www.theses.fr/2004INPT031H.

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Cette thèse porte sur un problème de mécanique spatiale, un transfert orbital à poussée faible, autour de la Terre, avec maximisation de la masse finale. La difficulté de ce problème vient des discontinuités de la commande optimale et du fait que les instants de commutations ne sont pas connus (nombre et localisation). La méthode du tir simple devenant particulièrement sensible à l'initialisation, on paramètre le critère du problème pour relier la minimisation de l'énergie à la minimisation de la consommation. La fonction de tir résultant de la paramétrisation définit alors une homotopie dont le chemin de zéros est suivi par une méthode de continuation différentielle. Une seconde homotopie, discrète celle-ci, permet d'affranchir complètement notre méthode de toute connaissance à priori sur la structure de la commande optimale, d'autant plus que le nombre de commutations peut être très important (plus de 1000 pour une poussée de 0. 1 N et un satellite de 1500 kg). Cette méthode de résolution est implantée dans un logiciel et appliquée avec succès a notre problème. Les résultats obtenus permettent de mettre en évidence un grand nombre de lois empiriques comme par exemple l'indépendance de l'évolution de la masse finale par rapport a la poussée maximale.
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Books on the topic "Minimisation problem"

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Kikuchi, Noboru. Contact problems in elasticity: A study of variational inequalities and finite element methods. Philadelphia: SIAM, 1988.

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JINGMIN. Computing Analysing Energy Minimisatiohb : Computing and Analysing Energy Minimisation Problems in Liquid Crystals: Implementation Using Firedr. World Scientific Publishing Co Pte Ltd, 2023.

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Kikuchi, N., and J. Tinsley Oden. Contact Problems in Elasticity: A Study of Variational Inequalities and Finite Element Methods (Studies in Applied and Numerical Mathematics). Society for Industrial Mathematics, 1995.

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Book chapters on the topic "Minimisation problem"

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Ponter, Alan R. S. "The Ratchet Limit—A Coupled Dual Minimisation Problem." In Limit State of Materials and Structures, 1–18. Dordrecht: Springer Netherlands, 2013. http://dx.doi.org/10.1007/978-94-007-5425-6_1.

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Baatar, Davaatseren, Mohan Krishnamoorthy, and Andreas T. Ernst. "A Triplet-Based Exact Method for the Shift Minimisation Personnel Task Scheduling Problem." In Algorithms - ESA 2015, 59–70. Berlin, Heidelberg: Springer Berlin Heidelberg, 2015. http://dx.doi.org/10.1007/978-3-662-48350-3_6.

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Hutchings, Matthew, and Bertrand Gauthier. "Local Optimisation of Nyström Samples Through Stochastic Gradient Descent." In Machine Learning, Optimization, and Data Science, 123–40. Cham: Springer Nature Switzerland, 2023. http://dx.doi.org/10.1007/978-3-031-25599-1_10.

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AbstractWe study a relaxed version of the column-sampling problem for the Nyström approximation of kernel matrices, where approximations are defined from multisets of landmark points in the ambient space; such multisets are referred to as Nyström samples. We consider an unweighted variation of the radial squared-kernel discrepancy (SKD) criterion as a surrogate for the classical criteria used to assess the Nyström approximation accuracy; in this setting, we discuss how Nyström samples can be efficiently optimised through stochastic gradient descent. We perform numerical experiments which demonstrate that the local minimisation of the radial SKD yields Nyström samples with improved Nyström approximation accuracy in terms of trace, Frobenius and spectral norms.
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Klement, Sascha, and Thomas Martinetz. "On the Problem of Finding the Least Number of Features by L1-Norm Minimisation." In Lecture Notes in Computer Science, 315–22. Berlin, Heidelberg: Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-21735-7_39.

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Fages, Jean-Guillaume, and Tanguy Lapègue. "Filtering AtMostNValue with Difference Constraints: Application to the Shift Minimisation Personnel Task Scheduling Problem." In Lecture Notes in Computer Science, 63–79. Berlin, Heidelberg: Springer Berlin Heidelberg, 2013. http://dx.doi.org/10.1007/978-3-642-40627-0_8.

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Cheung, Michael Tow, and David W. K. Yeung. "Characterising the Solution of an Average Cost Minimisation Problem with Returns to Scale Measures and a Decomposition Technique." In Operations Research ’91, 380–83. Heidelberg: Physica-Verlag HD, 1992. http://dx.doi.org/10.1007/978-3-642-48417-9_104.

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Aubin, Jean-Pierre. "Minimisation Problems: General Theorems." In Optima and Equilibria, 9–19. Berlin, Heidelberg: Springer Berlin Heidelberg, 1998. http://dx.doi.org/10.1007/978-3-662-03539-9_2.

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Aubin, Jean-Pierre. "Minimisation Problems: General Theorems." In Optima and Equilibria, 9–18. Berlin, Heidelberg: Springer Berlin Heidelberg, 1993. http://dx.doi.org/10.1007/978-3-662-02959-6_2.

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Barba, Paolo Di. "Inverse Problems and Error Minimisation." In Lecture Notes in Electrical Engineering, 5–25. Dordrecht: Springer Netherlands, 2009. http://dx.doi.org/10.1007/978-90-481-3080-1_2.

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Aubin, Jean-Pierre. "Conjugate Functions and Convex Minimisation Problems." In Optima and Equilibria, 35–56. Berlin, Heidelberg: Springer Berlin Heidelberg, 1998. http://dx.doi.org/10.1007/978-3-662-03539-9_4.

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Conference papers on the topic "Minimisation problem"

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Katebi, M. R., M. J. Grimble, and J. Wilkie. "Ship Steering Control Problem Performance Criterion for Energy Minimisation." In 1986 American Control Conference. IEEE, 1986. http://dx.doi.org/10.23919/acc.1986.4789119.

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Fregolent, Annalisa, and Walter D’Ambrogio. "Evaluation of Different Strategies in the Parametric Identification of Dynamic Models." In ASME 1997 Design Engineering Technical Conferences. American Society of Mechanical Engineers, 1997. http://dx.doi.org/10.1115/detc97/vib-4154.

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Abstract In the present paper, two different updating techniques are compared: the FRU-IT method, based on the minimisation of the force residual through a deterministic approach, and the GAME-UP method based on the minimisation of the output residual, using genetic algorithms. FRU-IT method, as most of the deterministic approaches presented in the literature, is strongly affected by measurement errors, that propagate in the solution and require sophisticated regularisation techniques. The use of genetic algorithms, that find the solution in a heuristic way by simulating an evolution process and require only the definition of fitness indicators, allows to bypass this problem. Results, obtained by solving an experimental test case, confirm that the use of genetic algorithms is a valid alternative to traditional methods.
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Porter, Brian, Samir S. Mohamed, and Bamidele A. Sangolola. "Genetic Design of Dynamically Optimal Four-Bar Linkages." In ASME 1994 Design Technical Conferences collocated with the ASME 1994 International Computers in Engineering Conference and Exhibition and the ASME 1994 8th Annual Database Symposium. American Society of Mechanical Engineers, 1994. http://dx.doi.org/10.1115/detc1994-0220.

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Abstract It Is shown in this paper that, once the problem of designing dynamically optimal mechanisms is formulated as a constrained minimisation problem, genetic algorithms provide a procedure for solving this design problem which is very powerful but also very simple. These general results are illustrated by the genetic optimisation of a particular four-bar linkage that was previously optimised non-genetlcally. However, It is pointed out that the genetic design methodology described in this paper can in principle be used to minimise any desired combination of forces and couples in any mechanism.
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Kurup, Nikhil G., and K. S. Vijula Grace. "Optimisation Algorithms for Deep Learning Method: A Review with a Focus on Financial Applications." In 2nd International Conference on Modern Trends in Engineering Technology and Management. AIJR Publisher, 2023. http://dx.doi.org/10.21467/proceedings.160.37.

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In a variety of fields including financial applications like stock market analysis deep learning has achieved amazing success in producing precise forecasts. To train deep learning models for financial forecasts, however, is a difficult undertaking that calls for careful consideration of a variety of hyperparameters and optimisation strategies. Optimisation is a technique that is part of mathematics and is used to solve analytical and numerical problems in minimisation and maximisation of functions. It is thus used for getting improved prediction in terms of quality and performance. In this paper we discuss different techniques like SGD, AdaGram and others, that have proven effective in improving the convergence and generalization performance of deep learning models in finance. Here we focus on financial applications where deep learning algorithms are used for the problem solving were optimization is also a part.
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Tajdari, Farzam, Christiaan Eijck, Felix Kwa, Christiaan Versteegh, Toon Huysmans, and Yu Song. "Optimal Position of Cameras Design in a 4D Foot Scanner." In ASME 2022 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2022. http://dx.doi.org/10.1115/detc2022-89145.

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Abstract Optical motion capturing explains the three-Dimensional (3D) position estimation of points through triangulation employing several depth cameras. Prosperous performance relies on level of visibility of points from different cameras and the overlap of captured meshes in-between. Generally, the accuracy of the estimation is practically based on the camera parameters e.g., location and orientations. Accordingly, the camera network configurations play a key role in the quality of the estimated mesh. This paper proposes an optimal approach for camera placement based on characteristics of a depth camera D435i - Intel RealSense. The optimal problem includes a cost function that contains several minimisation and maximisation terms. The minimisation terms are distance of the cameras to the center of the scanning object, resolution error, and sparsity. And the maximisation terms are distance between each two pair of cameras, percent of captured point from an object, and the level of overlap between cameras. The object is designed based on practical experiments of human walking and is a bounding box around one step of dynamic foot work-space from heel strike posture to toe-off posture. The accuracy and robustness of the algorithms are assessed via experiment measurement, and sensitivity to the number of cameras is investigated. Accordingly, the experiment results determined that the scanning accuracy can be as high as 2.5 % based on a reference scan with a high-end scanner (Artec Eva).
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Goyder, Hugh G. D., and Damien P. T. Lancereau. "Methods for the Measurement of Non-Linear Damping and Frequency in Built-Up Structures." In ASME 2017 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2017. http://dx.doi.org/10.1115/detc2017-67007.

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Two key properties of a vibrating structure are the frequencies at which it resonates and its ability to absorb energy. For a linear structure, these properties are characterised by the natural frequencies and the damping ratios. For nonlinear systems, such properties may not exist and equivalents must be sought. A method of measuring equivalent properties has been developed for nonlinear systems by examining the decaying vibration time history following excitation of the system. In a first stage, the time history is filtered to separate out a frequency range of interest. In the second stage, which is the main concern of this paper, instantaneous values of natural frequencies and damping ratios are extracted from the decaying time history by means of a curve fitting process. The curve fitting involves finding four parameters two of which are the instantaneous natural frequency and damping ratio and two more which account for the amplitude and phase. The curve fitting is a minimisation process which is divided into two stages. For each minimisation step, the amplitude and phase are extracted first. It is shown that this may be done in a one-step process. Next the frequency and damping are determined. This is found to be a straightforward although more difficult process. The key to simplifying the problem is to recast the model in a favourable form that reduces the curve fitting process from one of finding four parameters to finding just two. The procedure is found to be robust and capable of detailed investigation.
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Gobbi, Massimiliano. "Optimal and Robust Design of Ground Vehicle Systems." In ASME 8th Biennial Conference on Engineering Systems Design and Analysis. ASMEDC, 2006. http://dx.doi.org/10.1115/esda2006-95471.

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A new approach for the design of vehicle subsystems is addressed in the paper. The new approach is based not only on the theory of multi-objective optimisation but also on robust design. The method is characterised both by the optimisation of the objective functions (corresponding to system performance indices) and by the reduction (or minimisation) of the sensitivity (variance) of the performance indices to stochastic perturbations. Such variances are computed (very quickly) by means of an original procedure based on the global approximation of the objective functions. Additionally, with respect to the mentioned features, the new approach is based on both a special study to explore all of the feasible design solutions, and on a global sensitivity procedure to analyse (in a stochastic context) the influence of each design variable on each objective function. Pareto-optimal design solutions for different levels of “robustness” can be computed in a very short time. The optimisation method has been tested on a relatively simple problem and applied with successful results to a complex design problem related to vehicle design.
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Fam, Mei Ling, Hoon Kiang Tan, Dimitrios Konovessis, and Lin Seng Ong. "A Review of Offshore Decommissioning Regulations in Three Countries: Strengths and Weaknesses." In ASME 2017 36th International Conference on Ocean, Offshore and Arctic Engineering. American Society of Mechanical Engineers, 2017. http://dx.doi.org/10.1115/omae2017-62596.

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The decommissioning of offshore structures around the world will be a persisting problem in the coming decades as many existing structures will exceed their design life, or when the reservoirs are depleted. This paper examines an overview of regulations in countries deemed to be more experienced in decommissioning such as the UK, Norway and the USA. The regulations were identified in terms of three areas: the legal, technical and financial security framework. It is concluded that the majority of the regulations covering the technical section are similar. The major differences are between two overarching philosophies — one that is more prescriptive with stricter requirements and another that is more flexible with a goal-setting regime. Non-technical aspects of decommissioning appear to attract increasing attention from governments, such as decommissioning financial capability, minimisation of costs while meeting regulatory requirements, transfer of liability if other decommissioning options are accepted, and the movement of wastes from offshore to onshore and their subsequent disposal.
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Voie, Per Erlend, and Nils Sødahl. "Optimisation of Steel Catenary Risers." In ASME 2013 32nd International Conference on Ocean, Offshore and Arctic Engineering. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/omae2013-10107.

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The riser system is a vital component of deep water floating production installations. Field specific optimised solutions are generally required to obtain a technical solution fit for purpose and to secure an economic field development. In some cases, the riser system is a potential technology stopper preventing use of existing field proven floater/station keeping solutions for new applications. One such example is operation of large diameter steel catenary risers (SCR) from floating production units in harsh environmental conditions. This study is focused on methodology for optimisation of riser systems by use of a mathematical optimisation scheme. An optimisation problem may formally be described as minimisation of a function in several variables (objective function) subjected to additional constraints. For the first time the general optimisation framework Optima is outlined allowing for use of standard riser analysis software for evaluation of objective function and constraints. Principles for selection of objective function and constraints are discussed for practical design applications with reference to design codes. Finally, an optimisation study of a steel riser for deep water and harsh environment is presented.
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Hicks, R. A., M. Whiteman, and C. W. Wilson. "The Effect of the Fuel Injector Internal Geometry Upon the Primary Zone Aerodynamics." In ASME 1998 International Gas Turbine and Aeroengine Congress and Exhibition. American Society of Mechanical Engineers, 1998. http://dx.doi.org/10.1115/98-gt-232.

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One of the major aims of research in gas turbine combustor systems is the minimisation of non-desirable emissions. The primary method of reducing pollutants such as soot and NOx has been to run the combustion primary zone lean. Unfortunately, this causes problems when the combustor is run under idle and relight conditions as the primary zone air fuel ratio (AFR) can exceed the flammability limit. Altering this AFR directly affects the primary zone aerodynamics through changes in the spray profile. One method of determining the influence of changes in AFR upon the primary zone is to use Computational Fluid Dynamic (CFD) models. However, to model the flow through an air-blast fuel injector and accurately predict the resulting primary zone aerodynamics requires hundreds of thousands, if not millions, of cells. Therefore, with current computer capabilities simplifications need to be made. One simplification is to model the primary zone as a 2-D case. This reduces the number of cells to a computationally solvable level. However, by reducing the problem to 2-D the ability to accurately model air-blast fuel injectors is lost as they are intrinsically 3-D devices. Therefore, it is necessary to define boundary conditions for the fuel injector. Currently, due to difficulties in obtaining experimental measurements inside a air-blast fuel injector, these boundary conditions are often derived using semi-empirical methods. This paper presents and compares two such models; the model proposed by Crocker et al. in 1996 and one developed at DERA specifically for modelling air-blast fuel injectors. The work also highlights the importance of the often neglected radial component upon the primary zone aerodynamics.
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