Journal articles: 'Lagrange optimisation'

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Xu, Yihong, and Chuanxi Zhu. "On super efficiency in set-valued optimisation in locally convex spaces." Bulletin of the Australian Mathematical Society 71, no. 2 (April 2005): 183–92. http://dx.doi.org/10.1017/s0004972700038168.

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The set-valued optimisation problem with constraints is considered in the sense of super efficiency in locally convex linear topological spaces. Under the assumption of nearly cone-subconvexlikeness, by applying the separation theorem for convex sets, Kuhn-Tucker and Lagrange necessary conditions for the set-valued optimisation problem to attain its super efficient solutions are obtained. Also, Kuhn-Tucker and Lagrange sufficient conditions are derived. Finally two kinds of unconstrained programs equivalent to set-valued optimisation problems are established.

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Vaidogas, E. R. "ON RELIABILITY-BASED STRUCTURAL OPTIMISATION USING STOCHASTIC QUASIGRADIENT METHODS/ZUR ZUVERLÄSSIGKEITSTHEORETISCH GESTÜTZTEN TRAGWERKS-OPTIMIERUNG MIT VERFAHREN DER STOCHASTISCHEN QUASIGRA-DIENTEN." JOURNAL OF CIVIL ENGINEERING AND MANAGEMENT 1, no. 2 (June 30, 1995): 43–64. http://dx.doi.org/10.3846/13921525.1995.10531512.

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Methodical aspects of the reliability-based structural optimisation using stochastic quasigradient methods are considered. For an example of the simply supported reinforced concrete beam, the employment of the Lagrange multiplier method that belongs to the class of stochastic quasigradient methods is demonstrated. The classical optimum design goal to minimise structural cost or weight under the constraint on the structural failure probability is taken for consideration. Optimisation problems solved with the Lagrangemultiplier method are formulated in form of general stochastic programming problem. The mathematical expectation of the concrete volume reduced with respect to the in-place cost of the beam materials is taken as the objective function. Constraint function is the limitation placed on the beam failure probability. The beam is considered as a series structural system. Values of the prescribed allowable failure probability belongs to the interval in which the estimation of the failure probabilities by the simple Monte-Carlomethod is possible with an acceptable confidence. The time-independent case as well as the time-dependent one is considered in the optimisation problems. The generalisation on the time-dependent case is undertaken through the introduction into the constraint function of the quasi-linear distribution law of the random variables. In the time-dependent case, the objective function is associated with beginning and the constraint function with end of the service period. An expression of the stochastic gradient based on the differentiation under the integral sign is used for calculations with the Lagrange multiplier method. The stochastic gradient used is computationally more effective in comparison with stochastic finite-difference formulae usual in stochastic quasigradient methods because it requires only one computation of the structure in search iteration of the optimisation process. Three rules based on statistical argumentation are used for the stopping of the seat according to the procedure of the Lagrange multiplier method. The optimising of the beam shows that the Lagrange multiplier method is applicable for the optimal design of structures in that cases when the structural reliability can be estimated by means of the simple Monte-Carlo method. Additional research is needed for integration in the Lagrange multiplier method of statistical simulation techniques for the estimation of small structural failure probabilities.

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Li, Taiyong, and Yihong Xu. "The Strictly Efficient Subgradient of Set-Valued Optimisation." Bulletin of the Australian Mathematical Society 75, no. 3 (June 2007): 361–71. http://dx.doi.org/10.1017/s0004972700039290.

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The subgradient, under strict efficiency, of a set-valued mapping is developed, and the existence of the subgradient is proved. Optimality conditions in terms of Lagrange multipliers for a strictly efficient point are established in the general case and in the case with ic-cone-convexlike data.

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Antczak, Tadeusz. "Saddle point criteria and duality in multiobjective programming via an η-approximation method." ANZIAM Journal 47, no. 2 (October 2005): 155–72. http://dx.doi.org/10.1017/s1446181100009962.

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AbstractIn this paper, Antczak's η-approximation approach is used to prove the equivalence between optima of multiobjective programming problems and the η-saddle points of the associated η-approximated vector optimisation problems. We introduce an η-Lagrange function for a constructed η-approximated vector optimisation problem and present some modified η-saddle point results. Furthermore, we construct an η-approximated Mond-Weir dual problem associated with the original dual problem of the considered multiobjective programming problem. Using duality theorems between η-approximation vector optimisation problems and their duals (that is, an η-approximated dual problem), various duality theorems are established for the original multiobjective programming problem and its original Mond-Weir dual problem.

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Ringis, Daniel J., François Pitié, and Anil Kokaram. "Per Clip Lagrangian Multiplier Optimisation for HEVC." Electronic Imaging 2020, no. 10 (January 26, 2020): 136–1. http://dx.doi.org/10.2352/issn.2470-1173.2020.10.ipas-136.

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The majority of internet traffic is video content. This drives the demand for video compression in order to deliver high quality video at low target bitrates. This paper investigates the impact of adjusting the rate distortion equation on compression performance. An constant of proportionality, k, is used to modify the Lagrange multiplier used in H.265 (HEVC). Direct optimisation methods are deployed to maximise BD-Rate improvement for a particular clip. This leads to up to 21% BD-Rate improvement for an individual clip. Furthermore we use a more realistic corpus of material provided by YouTube. The results show that direct optimisation using BD-rate as the objective function can lead to further gains in bitrate savings that are not available with previous approaches.

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Góral, Ida, and Krzysztof Tchoń. "Lagrangian Jacobian Motion Planning: A Parametric Approach." Journal of Intelligent & Robotic Systems 85, no. 3-4 (July 13, 2016): 511–22. http://dx.doi.org/10.1007/s10846-016-0394-4.

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AbstractThis paper addresses the motion planning problem of nonholonomic robotic systems. The system’s kinematics are described by a driftless control system with output. It is assumed that the control functions are represented in a parametric form, as truncated orthogonal series. A new motion planning algorithm is proposed based on the solution of a Lagrange-type optimisation problem stated in the linear approximation of the parametrised system. Performance of the algorithm is illustrated by numeric computations for a motion planning problem of the rolling ball.

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Tizzi, S. "Polynomial series expansion for optimisation of wing plane structures in idealised critical flutter conditions." Aeronautical Journal 109, no. 1091 (January 2005): 23–33. http://dx.doi.org/10.1017/s0001924000000506.

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Abstract A numerical procedure, which utilises polynomial power series expansions for the optimisation of multipanel wing structures in idealised critical flutter conditions, is introduced and developed. It arises from the Rayleigh-Ritz method and employes trial polynomial describing functions both for the flexural displacement and for the thickness variation over the multipanel surface. An idealised structural plate model, according to the Kirchhoff’s theory, together with a linearised supersonic aerodynamic approach, are supposed. The classical Euler-Lagrange optimality criterion, based on variational principles, has been utilised for the optimisation operations, where by imposing the stationary conditions of the Lagrangian functional expression, a nonlinear algebraic equations system is obtained, whose solution is found by an appropriate algorithm. By utilising an iterative process it is possible to reach the reference structure critical conditions, with an optimised thickness distribution throughout the multipanel surface. The final part of the work consists in searching the minimum weight of the multipanel planform wing structure with optimised thickness profile vs the flutter frequency, considered as a variable imput parameter, for fixed flutter speed and equal to the critical one of the reference uniform structure.

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Sommerfeld, Martin, and Silvio Schmalfuß. "Analysis and optimisation of particle mixing performance in fluid phase resonance mixers based on Euler/Lagrange calculations." Advanced Powder Technology 31, no. 1 (January 2020): 139–57. http://dx.doi.org/10.1016/j.apt.2019.10.006.

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Warner, Paul. "Use of Lagrange Multipliers to Provide an Approximate Method for the Optimisation of a Shield Radius and Contents." EPJ Web of Conferences 153 (2017): 06012. http://dx.doi.org/10.1051/epjconf/201715306012.

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Krzyżaniak, Stanisław. "Optimisation of the stock structure of a single stock item taking into account stock quantity constraints, using a lagrange multiplier." Logforum 18, no. 2 (June 30, 2022): 261–69. http://dx.doi.org/10.17270/j.log.2022.730.

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Euttamarajah, Shornalatha, Yin Hoe Ng, and Chee Keong Tan. "Energy-Efficient Joint Base Station Switching and Power Allocation for Smart Grid Based Hybrid-Powered CoMP-Enabled HetNet." Future Internet 13, no. 8 (August 17, 2021): 213. http://dx.doi.org/10.3390/fi13080213.

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With the rapid proliferation of wireless traffic and the surge of various data-intensive applications, the energy consumption of wireless networks has tremendously increased in the last decade, which not only leads to more CO2 emission, but also results in higher operating expenditure. Consequently, energy efficiency (EE) has been regarded as an essential design criterion for future wireless networks. This paper investigates the problem of EE maximisation for a cooperative heterogeneous network (HetNet) powered by hybrid energy sources via joint base station (BS) switching (BS-Sw) and power allocation using combinatorial optimisation. The cooperation among the BSs is achieved through a coordinated multi-point (CoMP) technique. Next, to overcome the complexity of combinatorial optimisation, Lagrange dual decomposition is applied to solve the power allocation problem and a sub-optimal distance-based BS-Sw scheme is proposed. The main advantage of the distance-based BS-Sw is that the algorithm is tuning-free as it exploits two dynamic thresholds, which can automatically adapt to various user distributions and network deployment scenarios. The optimal binomial and random BS-Sw schemes are also studied to serve as benchmarks. Further, to solve the non-fractional programming component of the EE maximisation problem, a low-complexity and fast converging Dinkelbach’s method is proposed. Extensive simulations under various scenarios reveal that in terms of EE, the proposed joint distance-based BS-Sw and power allocation technique applied to the cooperative and harvesting BSs performs around 15–20% better than the non-cooperative and non-harvesting BSs and can achieve near-optimal performance compared to the optimal binomial method.

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Liu, Yong, and Huan-huan Zhao. "Dynamic information aggregation decision-making methods based on variable precision rough set and grey clustering." Grey Systems: Theory and Application 4, no. 2 (July 29, 2014): 347–61. http://dx.doi.org/10.1108/gs-04-2014-0010.

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Purpose – The purpose of this paper is to construct a dynamic information aggregation decision-making model based on variable precision rough set. Design/methodology/approach – To deal with the dynamic decision-making problems, the grey relational analysis method, grey fixed weight clustering based on the centre triangle whitening weight function and maximum entropy principle is used to establish the dynamic information aggregation decision-making model based on variable precision rough set. The method, to begin with, the grey relational analysis method is used to determine the attributes weights of each stage; taking the proximity of the attribute measurement value and positive and negative desired effect value and the uncertainty of time weight into account, a multi-objective optimisation model based on maximum entropy principle is established to solve the model with Lagrange multiplier method, so that time weights expression are acquired; what is more, the decision-making attribute is obtained by grey fixed weight clustering based on the centre triangle whitening weight function, so that multi-decision-making table with dynamic characteristics is established, and then probabilistic decision rules from multi-criteria decision table are derived by applying variable precision rough set. Finally, a decision-making model validates the feasibility and effectiveness of the model. Findings – The results show that it the proposed model can well aggregate the multi-stage dynamic decision-making information, realise the extraction of decision-making rules. Research limitations/implications – The method exposed in the paper can be used to deal with the decision-making problems with the multi-stage dynamic characteristics, and decision-making attributes contain noise data and the attribute values are interval grey numbers. Originality/value – The paper succeeds in realising both the aggregation of dynamic decision-making information and the extraction of decision-making rules.

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Raue, Erich, Hans-Georg Timmler, and Robert Garke. "ON THE PHYSICALLY NON‐LINEAR ANALYSIS OF CYCLIC LOADED REINFORCED CONCRETE CROSS‐SECTIONS WITH MATHEMATICAL OPTIMISATION." JOURNAL OF CIVIL ENGINEERING AND MANAGEMENT 15, no. 2 (June 30, 2009): 189–95. http://dx.doi.org/10.3846/1392-3730.2009.15.189-195.

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In the paper, experimental results of tension member tests are used as a basis from which to develop an extended tension stiffening model for reinforced concrete, with emphasis on the specific concrete damage and the developments of residual deformations depending on the structural loading. Two characteristics are contained in the proposed model: one describes the residual deformation behaviour along the reinforcement accounting for the cracks that cannot be closed completely, while the other describes the degradation of the concrete stiffness. Within context of non‐linear analysis, the model is incorporated into an analytical approach, based on the LAG RANGE principle of minimum of total potential energy. The mechanical problem is solved with the application of the mathematical optimisation, using energy principles formulated as a kinematic formulation and transforming them into non‐linear optimisation problems. It was demonstrated, that this approach is eminently suitable for analysing pre‐damaged or pre‐loaded reinforced concrete cross‐sections under cyclic loading. Santrauka Pateikti tempiamųjų gelžbetoninių elementų eksperimentinių tyrimų rezultatai. Remiantis šiais rezultatais pasiūlytas supleišėjusio tempiamojo betono modelis, kuriame įvertinama betono pažaidų ir liekamųjų deformacijų didėjimo įtaka tempiamųjų gelžbetoninių elementų elgsenai. Modelis susideda iš dviejų komponentų: pirmasis aprašo išilginių liekamųjų deformacijų armatūroje kitimą, o antrasis betono įtakos elemento skerspjūvio deformacijoms mažėjimą. Netiesinė analizė atliekama taikant analizinį algoritmą, kuris pagrįstas Lagranžo potencinės energijos minimalumo principu. Mechaninė problema išspręsta taikant matematinį optimizavimą ir energinius principus. Pastarieji aprašyti kinematinėmis formuluotėmis jas perkeliant į netiesinio optimizavimo uždavinio algoritmus. Parodyta, kad pasiūlytas algoritmas gerai tinka cikline apkrova veikiamiems gelžbetoniniams elementams analizuoti.

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14

DUFRESNE, M., S. ISEL, A. BENESCH, and D. HILLIGARDT. "Évaluation et optimisation des performances de décantation de bassins de stockage des eaux pluviales par mécanique des ﬂuides numérique." Techniques Sciences Méthodes, no. 12 (January 20, 2020): 45–59. http://dx.doi.org/10.36904/tsm/201912045.

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Cet article présente la mise en œuvre d’un modèle de mécanique des ﬂuides numérique pour évaluer les performances de décantation de trois bassins de stockage des eaux pluviales situés dans le sud-ouest de l’Allemagne et qui ne respectent pas les règles de l’art allemandes (rapport longueur sur largeur trop petit, entrée en virage et présence d’un siphon en sortie). Après la modélisation hydraulique 3D de l’écoulement, un suivi lagrangien des particules en suspension est mis en œuvre afin d’évaluer l’abattement des bassins pour l’ensemble des vitesses de chute. La comparaison avec la méthode de Hazen permet de montrer que cette dernière est très imprécise pour évaluer les performances de décantation d’un bassin. En matière de conception, cette étude permet de montrer que les performances peuvent être améliorées en distribuant le débit d’entrée sur plusieurs orifices ou bien en mettant en place un déﬂecteur.

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Burman, Erik, Peter Hansbo, and Mats G. Larson. "The Augmented Lagrangian Method as a Framework for Stabilised Methods in Computational Mechanics." Archives of Computational Methods in Engineering, January 20, 2023. http://dx.doi.org/10.1007/s11831-022-09878-6.

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AbstractIn this paper we will present a review of recent advances in the application of the augmented Lagrange multiplier method as a general approach for generating multiplier-free stabilised methods. The augmented Lagrangian method consists of a standard Lagrange multiplier method augmented by a penalty term, penalising the constraint equations, and is well known as the basis for iterative algorithms for constrained optimisation problems. Its use as a stabilisation methods in computational mechanics has, however, only recently been appreciated. We first show how the method generates Galerkin/Least Squares type schemes for equality constraints and then how it can be extended to develop new stabilised methods for inequality constraints. Application to several different problems in computational mechanics is given.

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Rassaki, Abdoul, and Andre Nel. "Optimizing Capacity Assignment in Multiservice MPLS Networks." South African Computer Journal 29, no. 1 (July 8, 2017). http://dx.doi.org/10.18489/sacj.v29i1.393.

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The general Multiprotocol Label Switch (MPLS) topology optimisation problem is complex and concerns the optimum selection of links, the assignment of capacities to these links and the routing requirements on these links. Ideally, all these are jointly optimised, leading to a minimum cost network which continually meets given objectives on network delay and throughput. In practice, these problems are often dealt with separately and a solution iterated. In this paper, we propose an algorithm that computes the shortest routes, assigns optimal flows to these routes and simultaneously determines optimal link capacities. We take into account the dynamic adaptation of optimal link capacities by considering the same Quality of Service (QoS) measure used in the flow assignment problem in combination with a blocking model for describing call admission controls (CAC) in multiservice broadband telecommunication networks. The main goal is to achieve statistical multiplexing advantages with multiple traffic and QoS classes of connections that share a common trunk present. We offer a mathematical programming model of the problem and proficient solutions which are founded on a Lagrangean relaxation of the problem. Experimental findings on 2-class and 6-class models are reported.

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Journal articles on the topic 'Lagrange optimisation'

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