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Existence of minimizers and necessary conditions in set-valued optimization with equilibrium constraints

Truong Q. Bao, Boris S. Mordukhovich (2007)

Applications of Mathematics

In this paper we study set-valued optimization problems with equilibrium constraints (SOPECs) described by parametric generalized equations in the form 0 ∈ G ( x ) + Q ( x ) , where both G and Q are set-valued mappings between infinite-dimensional spaces. Such models particularly arise from certain optimization-related problems governed by set-valued variational inequalities and first-order optimality conditions in nondifferentiable programming. We establish general results on the existence of optimal solutions under...

Existence of solutions to weak nonlinear bilevel problems via MinSup and d.c. problems

Abdelmalek Aboussoror, Abdelatif Mansouri (2008)

RAIRO - Operations Research

In this paper, which is an extension of [4], we first show the existence of solutions to a class of Min Sup problems with linked constraints, which satisfy a certain property. Then, we apply our result to a class of weak nonlinear bilevel problems. Furthermore, for such a class of bilevel problems, we give a relationship with appropriate d.c. problems concerning the existence of solutions.

Expected utility maximization and conditional value-at-risk deviation-based Sharpe ratio in dynamic stochastic portfolio optimization

Soňa Kilianová, Daniel Ševčovič (2018)

Kybernetika

In this paper we investigate the expected terminal utility maximization approach for a dynamic stochastic portfolio optimization problem. We solve it numerically by solving an evolutionary Hamilton-Jacobi-Bellman equation which is transformed by means of the Riccati transformation. We examine the dependence of the results on the shape of a chosen utility function in regard to the associated risk aversion level. We define the Conditional value-at-risk deviation ( C V a R D ) based Sharpe ratio for measuring...

Expériences with Stochastic Algorithms fir a class of Constrained Global Optimisation Problems

Abdellah Salhi, L.G. Proll, D. Rios Insua, J.I. Martin (2010)

RAIRO - Operations Research

The solution of a variety of classes of global optimisation problems is required in the implementation of a framework for sensitivity analysis in multicriteria decision analysis. These problems have linear constraints, some of which have a particular structure, and a variety of objective functions, which may be smooth or non-smooth. The context in which they arise implies a need for a single, robust solution method. The literature contains few experimental results relevant to such a need. We...

Experiments with variants of ant algorithms.

Thomas Stützle, Sebastian Linke (2002)

Mathware and Soft Computing

A number of extensions of Ant System, the first ant colony optimization (ACO) algorithm, were proposed in the literature. These extensions typically achieve much improved computational results when compared to the original Ant System. However, many design choices of Ant System are left untouched including the fact that solutions are constructed, that real-numbers are used to simulate pheromone trails, and that explicit pheromone evaporation is used. In this article we experimentally investigate...

Explicit polyhedral approximation of the Euclidean ball

J. Frédéric Bonnans, Marc Lebelle (2010)

RAIRO - Operations Research

We discuss the problem of computing points of IRn whose convex hull contains the Euclidean ball, and is contained in a small multiple of it. Given a polytope containing the Euclidean ball, we introduce its successor obtained by intersection with all tangent spaces to the Euclidean ball, whose normals point towards the vertices of the polytope. Starting from the L∞ ball, we discuss the computation of the two first successors, and give a complete analysis in the case when n=6.

Extended VIKOR as a new method for solving Multiple Objective Large-Scale Nonlinear Programming problems

Majeed Heydari, Mohammad Kazem Sayadi, Kamran Shahanaghi (2010)

RAIRO - Operations Research

The VIKOR method was introduced as a Multi-Attribute Decision Making (MADM) method to solve discrete decision-making problems with incommensurable and conflicting criteria. This method focuses on ranking and selecting from a set of alternatives based on the particular measure of “closeness” to the “ideal” solution. The multi-criteria measure for compromise ranking is developed from the l–p metric used as an aggregating function in a compromise programming method. In this paper, the VIKOR method...

Extension of reverse elimination method through a dynamic management of the tabu list

Saïd Hanafi, Arnaud Fréville (2001)

RAIRO - Operations Research - Recherche Opérationnelle

The Reverse Elimination Method (REM) is a dynamic strategy for managing the tabu list. It is based on logical interdependencies between the solutions encountered during recent iterations of the search. REM provides both a necessary and sufficient condition to prevent cycling. The purpose of this paper is first to incorporate in REM a chronological order rule when cycling is unavoidable, thereby assuring the finite convergence of Tabu Search. Secondly, we correct a generalization of REM, the so-called...

Extension of Reverse Elimination Method Through a Dynamic Management of the Tabu List

Saïd Hanafi, Arnaud Fréville (2010)

RAIRO - Operations Research

The Reverse Elimination Method (REM) is a dynamic strategy for managing the tabu list. It is based on logical interdependencies between the solutions encountered during recent iterations of the search. REM provides both a necessary and sufficient condition to prevent cycling. The purpose of this paper is first to incorporate in REM a chronological order rule when cycling is unavoidable, thereby assuring the finite convergence of Tabu Search. Secondly, we correct a generalization of REM, the so-called...

Currently displaying 121 – 140 of 157