Auswahl der wissenschaftlichen Literatur zum Thema „Méthodes Quasi-Newton“
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Zeitschriftenartikel zum Thema "Méthodes Quasi-Newton":
Gilbert, Jean Charles. „Mise à jour de la métrique dans les méthodes de quasi-Newton réduites en optimisation avec contraintes d'égalité“. ESAIM: Mathematical Modelling and Numerical Analysis 22, Nr. 2 (1988): 251–88. http://dx.doi.org/10.1051/m2an/1988220202511.
Dumont, Thierry. „Une méthode Quasi-Newton pour le calcul d'écoulements viscoélastiques“. ESAIM: Proceedings 2 (1997): 173–81. http://dx.doi.org/10.1051/proc:1997010.
Ngnepieba, Pierre, François Xavier Le Dimet, Alexis Boukong und Gabriel Nguetseng. „Parameters identification: an application to the Richards equation“. Revue Africaine de la Recherche en Informatique et Mathématiques Appliquées Volume 1, 2002 (14.10.2002). http://dx.doi.org/10.46298/arima.1833.
Dissertationen zum Thema "Méthodes Quasi-Newton":
SEGALAT, Philippe. „Méthodes de Points Intérieurs et de quasi-Newton“. Phd thesis, Université de Limoges, 2002. http://tel.archives-ouvertes.fr/tel-00005478.
Segalat, Philippe. „Méthodes de points intérieurs et de quasi-Newton“. Limoges, 2002. http://www.theses.fr/2002LIMO0041.
This thesis is interested in interior point and quasi-Newton methods in nonlinear optimization and with their implementation. One presents the code NOPTIQ using the limited memory BFGS formulas to solve large scale problems. The originality of this approach is the use of these formulas within the framework of interior point methods. The storage requirement and the computing cost of one iteration are then low. One shows that NOPTIQ is robust and that its performance are comparable with the reference codes 1-BFGS-B and LANCELOT. One presents also an infeasible algorithm using the preceding methods to solve a nonlinear problem with inequality constraints and linear equality constraints. The idea to penalize the problem using shift variables and a variant of the big-M method of linear programming. The q-superlinear convergence of the inner iterates and the global convergence of outer iterates are shown
Raynaud, Paul. „L'exploitation de la structure partiellement-séparable dans les méthodes quasi-Newton pour l'optimisation sans contrainte et l'apprentissage profond“. Electronic Thesis or Diss., Université Grenoble Alpes, 2024. http://www.theses.fr/2024GRALI021.
This thesis studies and improves the use of the partially-separable structure for unconstrained optimization, particularly for quasi-Newton methods and training neural networks.A partially-separable function is the sum of element functions, each of lower dimension than the total problem.Thus, the Hessian can be aggregated by separately approximating the Hessian of each element function with a dense matrix.These partitioned quasi-Newton methods are applicable to high-dimensional problems and maintain the sparse structure of the Hessian, unlike a limited-memory quasi-Newton method.In practice, these methods require fewer iterations than a limited-memory quasi-Newton method and are parallelizable by distributing computations related to the element functions.However, a comprehensive literature review on the subject has revealed some limitations, particularly when the dimension of the element functions is large.Additionally, the only open-source optimization software exploiting the partially-separable structure is unusable for inexperienced users, leaving only commercial software as an option.In this thesis, two solutions are proposed to address these shortcomings, along with an application of partially-separable optimization concepts to supervised learning of a neural network.The first contribution is a software suite based on an automatic detection of the partially-separable structure of a problem, i.e., retrieves each reduced-dimensional element function.Following this, partitioned data structures necessary for storing derivatives, or their approximations, are allocated and used to define partitioned quasi-Newton optimization methods.The entire suite is integrated into the "JuliaSmoothOptimizers" ecosystem, which gathers numerous tools for smooth optimization, including optimization algorithms that can therefore exploit the detected partial separability.The second contribution replaces the approximation of an element Hessian by a dense matrix with a limited-memory quasi-Newton linear operator.As a result, the memory cost of the total Hessian approximation is no longer quadratically related to the dimension of the element functions.A limited-memory partitioned quasi-Newton method is then applicable when the element functions are large.Each limited-memory partitioned quasi-Newton method has a proof of global convergence.Additionally, numerical results show that these methods outperform partitioned or limited-memory quasi-Newton methods when the elements are large.The final contribution examines the exploitation of the partially-separable structure during supervised training of a neural network.The optimization problem associated with training is generally not partially-separable.Therefore, a partially-separable loss function and a partitioned network architecture are introduced to make the training partially-separable.Numerical results combining these two contributions are competitive with standard architectures and loss functions according to state-of-the-art training methods.Moreover, this combination produces an additional parallelization scheme to existing methods for supervised learning.Indeed, the calculations of each element loss function can be distributed to a worker requiring only a fraction of the neural network to operate.Finally, a limited-memory partitioned quasi-Newton training is proposed.This training is empirically shown to be competitive with state-of-the-art training methods
Berenguer, Laurent. „Accélération de la convergence de méthodes numériques parallèles pour résoudre des systèmes d’équations différentielles linéaires et transitoires non linéaires“. Thesis, Lyon 1, 2014. http://www.theses.fr/2014LYO10194/document.
Solving differential equations (PDEs/ODEs/DAEs) is central to the simulation of physical phenomena. The increase in size and complexity of the models requires the design of methods that are robust and efficient in terms of computational time. The aim of this thesis is to design methods that accelerate the solution of differential equations by domain decomposition methods. We first consider Schwarz domain decomposition methods to solve large-scale linear systems arising from the discretization of PDEs. In order to accelerate the convergence of the Schwarz method, we propose an approximation of the error propagation operator. This approximation preserves the structure of the exact operator. A significant reduction of computational time is obtained for the groundwater flow problem in highly heterogeneous media. The second contribution concerns solving the sequence of linear systems arising from the time-integration of nonlinear problems. We propose two approaches, taking advantage of the fact that the Jacobian matrix does not change dramatically from one system to another. First, we apply Broyden’s update to the Restricted Additive Schwarz (RAS) preconditioner instead of recomputing the local LU factorizations. The second approach consists of dedicating processors to the asynchronous and partial update of the RAS preconditioner. Numerical results for the lid-driven cavity problem, and for a reaction-diffusion problem show that a super-linear speedup may be achieved. The last contribution concerns the simultaneous solution of nonlinear problems associated to consecutive time steps. We study the case where the Broyden method is used to solve these nonlinear problems. In that case, Broyden’s update of the Jacobian matrix may also be propagated from one time step to another. The parallelization through the time steps is also applied to the problem of finding a consistent initial guess for differential-algebraic equations
Nachaoui, Abdeljalil. „Contribution à l'analyse et à l'approximation des problèmes d'identification, de reconstruction et des systèmes d'équations elliptiques non linéaires“. Habilitation à diriger des recherches, Université de Nantes, 2002. http://tel.archives-ouvertes.fr/tel-00002635.
Kudawoo, Ayaovi Dzifa. „Problèmes industriels de grande dimension en mécanique numérique du contact : performance, fiabilité et robustesse“. Thesis, Aix-Marseille, 2012. http://www.theses.fr/2012AIXM4771/document.
This work deals with computational contact mechanics between deformable solids. The aim of this work is to improve the performance, the reliability and the robustness of the algorithms and numerical models set in Code_Aster which is finite element code developped by Électricité De France (EDF) for its engineering needs. The proposed algorithms are used to solve high dimensional industrial problems in order to optimize the computational running times. Several solutions techniques are available in the field of computational contact mechanics but they must take into account the difficulties coming from non-smooth aspects due to Signorini-Coulomb laws coupled to large deformations of bodies and material non linearities. Firstly the augmented Lagrangian formulation so-called « stabilized Lagrangian » is introduced. Successively, the mathematical properties of the discrete operators are highlighted and furthermore a novel energetic function is presented. Secondly the kinematical condition with regard to the normal unknowns are reinforced through unconstrained optimization techniques which result to a novel formulation which is so-called « non standard augmented Lagrangian formulation ». Three types of strategies are implemented in the code. The generalized Newton method is developped : it is a method in which all the non linearities are solved in one loop of iterations. The partial Newton method is an hybrid technique between the generalized Newton one and a fixed point method
Nguyen, Quoc Thong. „Modélisation probabiliste d’impression à l’échelle micrométrique“. Thesis, Lille 1, 2015. http://www.theses.fr/2015LIL10039/document.
We develop the probabilistic models of the print at the microscopic scale. We study the shape randomness of the dots that originates the prints, and the new models could improve many applications such as the authentication. An analysis was conducted on various papers, printers. The study shows a large variety of shape that depends on the printing technology and paper. The digital scan of the microscopic print is modeled in: the gray scale distribution, and the spatial binary process modeling the printed/blank spatial distribution. We seek the best parametric distribution that takes account of the distributions of the blank and printed areas. Parametric distributions are selected from a set of distributions with shapes close to the histograms and with the Kolmogorov-Smirnov divergence. The spatial binary model handles the wide diversity of dot shape and the range of variation of spatial density of inked particles. At first, we propose a field of independent and non-stationary Bernoulli variables whose parameters form a Gaussian power. The second spatial binary model encompasses, in addition to the first model, the spatial dependence of the inked area through an inhomogeneous Markov model. Two iterative estimation methods are developed; a quasi-Newton algorithm which approaches the maximum likelihood and the Metropolis-Hasting within Gibbs algorithm that approximates the minimum mean square error estimator. The performances of the algorithms are evaluated and compared on simulated images. The accuracy of the models is analyzed on the microscopic scale printings coming from various printers. Results show the good behavior of the estimators and the consistency of the models
Vaquez, Philippe. „Localisation de la rupture à l'aide des splines en plasticité parfaite“. Paris 11, 1986. http://www.theses.fr/1986PA112379.
This study presents the behaviour of Brevibacterium linens in a fermentor on a L-lactate and casamino acids medium. The first part consists of an experimental design used to point out the effect of 3 factors: the pH (7,5-8,5), the temperature (20-30°C) and the dissolved oxygen concentration (40-60% of the saturation), both of them controlled during the culture, on growth and metabolism parameters at different times: lag time, end of exponential growth, end of the falling back of growth and final time. The values of these times, the absorbance (D. O. ) of the culture, the concentration of lactate and amino acids, and produced ammonia at these times were analysed. The value of generation time was deduced from graphical response. The logistic law was used to improve growth data precision, and the following parameters were deduced: time to reach 2. 5, 35, and 80% of the maximal O. D. , value of this maximum, maximal and mean growth rate. Data obtained from the pH and dissolved oxygen controls at the same typical times were also analysed. The most important results were obtained from the variance analysis on the overall experimental conditions and on the generation time parameter: they showed an important quadratic effect of oxygen, an important interaction between the 3 factors, and positive effects. The generation time decreased between 40% and 50% of dissolved oxygen and increased beyond this level. The other parameters were less explained, but it appeared that the value of maximal growth is factors independent. The substrate consumption pointed out no factor effect, with the obtained precision, except a linear, quadratic and cubic effect of dissolved oxygen: tested at the levels 40 and 60%, this factor leads to incomplete substrate consumption, compared with the level 45-55%. But, is the maximal growth achieved in the case of these cultures? B. Linens produced ammonia which is absorbed with the amino acids, this fact pointed out by linear regressions statistically significant. A preferential consumption of a few amino acids (arginine, tyrosine and phenylalanine) has been detected, as ornithine production in some circumstances. His aroma production activities were pointed out qualitatively by sniffing. The freeze dryed suspension showed longer lag periods, and a greater oxygen consumption. The volumes of acid or alkali used to maintain the pH seemed to be more dependent on growth than on culture conditions. Some additional experiments presented in part 2, with mediums of different substrate concentrations showed that: - lactate is not limitant – some amino acids absorbed may be limitant, and decrease in growth rate may be explained by their removing – the low growth yields found in case of high lactate concentration medium may be explained by maintenances effects. Modelisation of biomass production and substrate consumption was tested, but the medium complexity prevented to do it
Roland, Nicolas. „Modélisation de la transition vers la turbulence d'écoulements en tuyau de fluides rhéofluidifiants par calcul numérique d'ondes non linéaires“. Thesis, Vandoeuvre-les-Nancy, INPL, 2010. http://www.theses.fr/2010INPL037N/document.
The transition to turbulence in pipe flows of shear-thinning fluids is studied theoretically. The method used is the computation of `exact coherent structures' that are tridimensional nonlinear waves. For this purpose a pseudo-spectral Petrov-Galerkin code is developped, which also allows to follow solution branches in the parameter space with continuation methods. This code is validated by recovering already published results in the Newtonian case, and by a consistency test in the non-Newtonian case. A spectral exponential convergence is obtained in all cases. This code is used to seek (guided by recent experimental results) new solutions of fundamental azimuthal wavenumber equal to 1,without success at the time being. On the contrary solutions with a fundamental azimuthal wavenumber equal to 2 and 3 are obtained by continuation from the Newtonian case. The shear-thinning effects induce, in terms of critical Reynolds numbers, a delay for the onset of these waves, as compared with the Newtonian case. This delay is characterized. An analogy is made with various experimental results that show a delay in the transition to turbulence, more precisely, in the onset of `puffs', in non-Newtonian fluids
Gilbert, Jean Charles. „Sur quelques problèmes d'identification et d'optimisation rencontrés en physique des plasmas“. Paris 6, 1986. http://www.theses.fr/1986PA066208.
Bücher zum Thema "Méthodes Quasi-Newton":
Dodu, J. C. Méthodes de quasi-Newton en optimisation non linéaire. Clamart: Electricité de France, Direction des études et recherches, Service études de réseaux, Département Méthodes d'optimisation et de simulation, 1990.