Split of an Optimization Variable in Game Theory

Aboulaïch, Rajae; Habbal, Abderrahmane; Moussaid, Noureddine

doi:10.1051/mmnp/20105720

Cited by 7 publications

(8 citation statements)

References 2 publications

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“…Proof. As u is a solution of problem (1), then u is the unique solution of the following minimization problem:…”

Section: Setting Of the Problemmentioning

confidence: 99%

“…The procedure described above does not require any great programming efforts in order to solve the compliance topology design problem. In the case of compliance optimization, the state or displacements u is the solution of the linear elasticity equation (1). We use P 2 × P 2 Lagrange finite elements to .…”

Section: Setting Of the Problemmentioning

confidence: 99%

“…We split the original design variable (thickness h) into two strategies [1,2], formally we denote h = (X, Y ) such that X, Y ∈ U h . The split of the variable h is to construct two allocation tables P and Q in {0, 1} n , where P i + Q i = 1, 1 ≤ i ≤ n and n is the size of h. Let I 12 = {1, ..., n} be a set of indices of cardinality n, I 1 a subset of I 12 of cardinality n 1 , and I 2 its complement of cardinality n 2 , that is to say…”

Section: Variable Thicknessmentioning

confidence: 99%

See 2 more Smart Citations

Study of different strategies for splitting variables in multidisciplinary topology optimization

Aboulaïch¹,

Habbal²,

Moussaid³

2014

ams

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This paper is devoted to the minimization of the thickness of an elastic structure under competitive loadings. We propose to determine an equilibrium thickness using game theory. We consider two loads exercised separately on two parts of the plate and we aim to optimize both compliances to deal with a multiloading optimization problem. Firstly, we the design variable is taken to be the thickness of the plate. In a second step, we assume that the thickness depends on two independent functions, that we consider as strategies. The multidisciplinary optimization problem is solved as a non-cooperative game and we determine a Nash equilibrium. Finally, some numerical simulations are presented and discuted.

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“…Proof. As u is a solution of problem (1), then u is the unique solution of the following minimization problem:…”

Section: Setting Of the Problemmentioning

confidence: 99%

Section: Setting Of the Problemmentioning

confidence: 99%

Section: Variable Thicknessmentioning

confidence: 99%

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Study of different strategies for splitting variables in multidisciplinary topology optimization

Aboulaïch¹,

Habbal²,

Moussaid³

2014

ams

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“…Notre but à présent est de montrer que le meilleur partage qu'on obtient par les deux algorithmes (AG1) et (AG2), donne un équilibre de Nash qui appartient au front de Pareto ou bien proche du front. Le front de Pareto est l'ensemble des solutions non dominées [1]. Lorsque le front de Pareto est convexe, on peut trouver tous ses points en minimisant…”

Section: Construction Deunclassified

Optimisation multicritère : Une approche par partage des variables

Aboulaïch¹,

Habbal

Moussaid³

2010

Revue Africaine De Recherche en Informatique Et Mathématiques Appliquées

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International audience We are interested here, in multi-criteria optimization problem using game theory. This problem will be treated by using a new algorithm for the splitting of territory in case of concurrent optimization, which presents a new formulation of Nash games between two players using two tables of allocations. Each player minimizes his cost function using the variables allocated by his own table. The two tables are given by an iterative algorithm. An image processing problem is addressed by using the proposed algorithms. On s’intéresse, dans ce travail, à un problème d’optimisation multi-critère en utilisant la théorie des jeux. Ce problème est traité en utilisant de nouveaux algorithmes pour le partage de territoire dans le cas d’une optimisation concourante. Il s’agit de présenter une formulation de jeux de Nash entre deux joueurs en utilisant deux tableaux d’allocation. Chaque joueur minimise sa fonction coût en agissant sur les variables allouées par son propre tableau. Les deux tableaux sont à construire grâce à un algorithme itératif. Une application de ces algorithmes à un problème de traitement d’images est considérée.

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“…CVaR has attractive theoretical properties: it controls the magnitude of losses beyond Valueat-Risk (VaR) and it is coherent (see for example Artzner 1999, Acerbi and Tasche 2002, Tasche 2002, Pflug 2000, Rockafellar and Uryasev 2002). In this paper we propose to solve the problem of portfolio selection, which is a multi-objective problem, first by using the NBI approach [8] based on SASP method [7], implemented in Matlab to find the efficient boundary, after we use the game theory [3,4] …”

Section: Introductionmentioning

confidence: 99%

The Mean-CVaR Model for Portfolio Optimization Using a Multi-Objective Approach and the Kalai-Smorodinsky Solution

et al. 2017

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Abstract. The purpose of this work is to present a model for portfolio multi-optimization, in which distributions are compared on the basis of tow statistics: the expected value and the Conditional Value-at-Risk (CVaR), to solve such a problem many authors have developed several algorithms, in this work we propose to find the efficient boundary by using the Normal Boundary Intersection approach (NBI) based on our proposed hybrid method SASP, since the considered problem is multi-objective, then we find the Kalai-smorodinsky solution.

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Split of an Optimization Variable in Game Theory

Cited by 7 publications

References 2 publications

Study of different strategies for splitting variables in multidisciplinary topology optimization

Study of different strategies for splitting variables in multidisciplinary topology optimization

Optimisation multicritère : Une approche par partage des variables

The Mean-CVaR Model for Portfolio Optimization Using a Multi-Objective Approach and the Kalai-Smorodinsky Solution

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