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Uniform Convergence of the Newton Method for Aubin Continuous Maps

Dontchev, Asen (1996)

Serdica Mathematical Journal

* This work was supported by National Science Foundation grant DMS 9404431.In this paper we prove that the Newton method applied to the generalized equation y ∈ f(x) + F(x) with a C^1 function f and a set-valued map F acting in Banach spaces, is locally convergent uniformly in the parameter y if and only if the map (f +F)^(−1) is Aubin continuous at the reference point. We also show that the Aubin continuity actually implies uniform Q-quadratic convergence provided that the derivative of f is Lipschitz...

Uniform value in dynamic programming

Jérôme Renault (2011)

Journal of the European Mathematical Society

We consider dynamic programming problems with a large time horizon, and give sufficient conditions for the existence of the uniform value. As a consequence, we obtain an existence result when the state space is precompact, payoffs are uniformly continuous and the transition correspondence is non expansive. In the same spirit, we give an existence result for the limit value. We also apply our results to Markov decision processes and obtain a few generalizations of existing results.

Uniqueness of optimal policies as a generic property of discounted Markov decision processes: Ekeland's variational principle approach

R. Israel Ortega-Gutiérrez, Raúl Montes-de-Oca, Enrique Lemus-Rodríguez (2016)

Kybernetika

Many examples in optimization, ranging from Linear Programming to Markov Decision Processes (MDPs), present more than one optimal solution. The study of this non-uniqueness is of great mathematical interest. In this paper the authors show that in a specific family of discounted MDPs, non-uniqueness is a “fragile” property through Ekeland's Principle for each problem with at least two optimal policies; a perturbed model is produced with a unique optimal policy. This result not only supersedes previous...

Use of semidefinite programming for solving the LQR problem subject to rectangular descriptor systems

Muhafzan (2010)

International Journal of Applied Mathematics and Computer Science

This paper deals with the Linear Quadratic Regulator (LQR) problem subject to descriptor systems for which the semidefinite programming approach is used as a solution. We propose a new sufficient condition in terms of primal dual semidefinite programming for the existence of the optimal state-control pair of the problem considered. The results show that semidefinite programming is an elegant method to solve the problem under consideration. Numerical examples are given to illustrate the results.

Utilisation de la programmation dynamique dans la modélisation de la pêcherie de la sardine au Maroc

Mohammed Abbad, Ghali M. Abdallaoui, Ghizlane Benomar (2004)

RAIRO - Operations Research - Recherche Opérationnelle

In this paper we use the dynamic programming approach to model the Moroccan sardine fishery system. We show how the elements of the dynamic programming method such as steps, states and actions are used. The proposed model determines the harvest quantity of sardine in each fishing season in order to maximize the total yield over some definite periods. Some numerical tests of the model, in the deterministic case, are presented and their results show that the approach used is promising. Besides determining...

Utilisation de la programmation dynamique dans la modélisation de la pêcherie de la sardine au Maroc

Mohammed Abbad, Ghali M. Abdallaoui, Ghizlane Benomar (2010)

RAIRO - Operations Research

Dans cet article on modélise le système de la pêche de la sardine au Maroc par la méthode de la programmation dynamique. On montre comment les éléments de la programmation dynamique tels que les étapes, états et actions sont utilisés. Le modèle proposé calcule la quantité de sardine à pêcher durant chaque saison de pêche dans le but de maximiser la récolte totale sur un certain nombre de périodes. Des tests, dans le cas déterministe, sont présentés et leurs résultats montrent que l'approche proposée...

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