An iterative algorithm of solution for quadratic minimization problem in Hilbert spaces.
An optimal algorithm with Barzilai-Borwein steplength and superrelaxation for QPQC problem
We propose a modification of MPGP algorithm for solving minimizing problem of strictly convex quadratic function subject to separable spherical constraints. This active set based algorithm explores the faces by the conjugate gradients and changes the active sets and active variables by the gradient projection with the Barzilai-Borwein steplength. We show how to use the algorithm for the solution of separable and equality constraints. The power of our modification is demonstrated on the solution...
An optimality system for finite average Markov decision chains under risk-aversion
This work concerns controlled Markov chains with finite state space and compact action sets. The decision maker is risk-averse with constant risk-sensitivity, and the performance of a control policy is measured by the long-run average cost criterion. Under standard continuity-compactness conditions, it is shown that the (possibly non-constant) optimal value function is characterized by a system of optimality equations which allows to obtain an optimal stationary policy. Also, it is shown that the...
An Optimization Procedure for Water Reservoir Planning
An Optimization Procedure for Water Reservoirs in Cascade
An optimized soft computing-based passage retrieval system
An overview of semi-infinite programming theory and related topics through a generalization of the alternative theorems.
We propose new alternative theorems for convex infinite systems which constitute the generalization of the corresponding to Gale, Farkas, Gordan and Motzkin. By means of these powerful results we establish new approaches to the Theory of Infinite Linear Inequality Systems, Perfect Duality, Semi-infinite Games and Optimality Theory for non-differentiable convex Semi-Infinite Programming Problem.
An Overview on Polynomial Approximation of NP-Hard Problems
An SMDP model for a multiclass multi-server queueing control problem considering conversion times
We address a queueing control problem considering service times and conversion times following normal distributions. We formulate the multi-server queueing control problem by constructing a semi-Markov decision process (SMDP) model. The mechanism of state transitions is developed through mathematical derivation of the transition probabilities and transition times. We also study the property of the queueing control system and show that optimizing the objective function of the addressed queueing control...
An SQP method for mathematical programs with complementarity constraints with strong convergence properties
We propose an SQP algorithm for mathematical programs with complementarity constraints which solves at each iteration a quadratic program with linear complementarity constraints. We demonstrate how strongly M-stationary solutions of this quadratic program can be obtained by an active set method without using enumeration techniques. We show that all limit points of the sequence of iterates generated by our SQP method are at least M-stationary.
An SQP trust region method for solving the discrete-time linear quadratic control problem
In this paper, a sequential quadratic programming method combined with a trust region globalization strategy is analyzed and studied for solving a certain nonlinear constrained optimization problem with matrix variables. The optimization problem is derived from the infinite-horizon linear quadratic control problem for discrete-time systems when a complete set of state variables is not available. Moreover, a parametrization approach is introduced that does not require starting a feasible solution...
An unbounded Berge's minimum theorem with applications to discounted Markov decision processes
This paper deals with a certain class of unbounded optimization problems. The optimization problems taken into account depend on a parameter. Firstly, there are established conditions which permit to guarantee the continuity with respect to the parameter of the minimum of the optimization problems under consideration, and the upper semicontinuity of the multifunction which applies each parameter into its set of minimizers. Besides, with the additional condition of uniqueness of the minimizer, its...
An unconstrained optimization technique for nonsmooth nonlinear complementarity problems.
Análisis de sensibilidad de las soluciones del problema lineal múltiple ordenado.
Partiendo del problema de programación lineal multiobjetivo bajo incertidumbre y definiendo la utilidad de una decisión factible x, como el k-ésimo valor ordenado del vector (c1x, c2x, ..., cpx), estudiamos en este trabajo el problema múltiple planteado en el caso de un conocimiento incompleto de los objetivos, así como la sensibilidad de una solución óptima en relación con dicho conocimiento parcial.
Análisis interactivo de las soluciones del problema lineal múltiple ordenado.
En este trabajo se estudian procedimientos para la elección entre las soluciones eficientes del Problema de Programación Lineal con Objetivos Múltiples, cuando el decisor manifiesta preferencias sobre ciertas ordenaciones de las valoraciones de las funciones objetivo, utilizándose como criterio de valoración global funciones basadas en el k-ésimo valor del vector de los objetivos ordenado en cada punto.Se desarrollan procedimientos para generar ordenaciones compatibles con la información del decisor....
Analyse de récession et résultats de stabilité d’une convergence variationnelle, application à la théorie de la dualité en programmation mathématique
Soit un espace de Banach de dual topologique . (resp. ) désigne l’ensemble des parties non vides convexes fermées de (resp. -fermées de ) muni de la topologie de la convergence uniforme sur les bornés des fonctions distances. Cette topologie se réduit à celle de la métrique de Hausdorff sur les convexes fermés bornés [16] et admet en général une représentation en terme de cette dernière [11]. De plus, la métrique qui lui est associée s’est révélée très adéquate pour l’étude quantitative...
Analyse de récession et résultats de stabilité d'une convergence variationnelle, application à la théorie de la dualité en programmation mathématique
Let X be a Banach space and X' its continuous dual. C(X) (resp. C(X')) denotes the set of nonempty convex closed subsets of X (resp. ω*-closed subsets of X') endowed with the topology of uniform convergence of distance functions on bounded sets. This topology reduces to the Hausdorff metric topology on the closed and bounded convex sets [16] and in general has a Hausdorff-like presentation [11]. Moreover, this topology is well suited for estimations and constructive approximations [6-9]. We...
Analyse de sensibilité pour les problèmes linéaires en variables 0-1
Cet article est un travail de synthèse autour de l’analyse de sensibilité pour les problèmes linéaires en variables 0-1. De nombreux aspects sont ainsi abordés : historique et formes d’analyse de sensibilité, exemples d’application, complexité, conditions d’optimalité, algorithmes et approches. Nous dressons par ailleurs quelques perspectives de recherche actuelles dans ce domaine.
Analyse de sensibilité pour les problèmes linéaires en variables 0-1
Cet article est un travail de synthèse autour de l'analyse de sensibilité pour les problèmes linéaires en variables 0-1. De nombreux aspects sont ainsi abordés : historique et formes d'analyse de sensibilité, exemples d'application, complexité, conditions d'optimalité, algorithmes et approches. Nous dressons par ailleurs quelques perspectives de recherche actuelles dans ce domaine.
Analyses de régression et programmation linéaire