Exact Penalization and Necessary Optimality Conditions for Multiobjective Optimization Problems with Equilibrium Constraints

A calmness condition for a general multiobjective optimization problem with equilibrium constraints is proposed. Some exact penalization properties for two classes of multiobjective penalty problems are established and shown to be equivalent to the calmness condition. Subsequently, a Mordukhovich stationary necessary optimality condition based on the exact penalization results is obtained. Moreover, some applications to a multiobjective optimization problem with complementarity constraints and a multiobjective optimization problem with weak vector variational inequality constraints are given

Optimality and duality for a class of nonsmooth fractional multiobjective optimization problems (Nonlinear Analysis and Convex Analysis)

In this paper, we establish necessary optimality conditions for (weakly) efficient solutions of a nonsmooth fractional multiobjective optimization problem with inequality and equality constraints by employing some advanced tools of variational analysis and generalized differentiation. Sufficient optimality conditions for such solutions to the considered problem are also provided by means of introducing (strictly) convex-affine functions. Along with optimality conditions, we formulate a dual problem to the primal one and explore weak, strong and converse duality relations between them under assumptions of (strictly) convex-affine functions

Proper efficiency and duality for a new class of nonconvex multitime multiobjective variational problems

In this paper, a new class of generalized of nonconvex multitime multiobjective variational problems is considered. We prove the sufficient optimality conditions for efficiency and proper efficiency in the considered multitime multiobjective variational problems with univex functionals. Further, for such vector variational problems, various duality results in the sense of Mond-Weir and in the sense of Wolfe are established under univexity. The results established in the paper extend and generalize results existing in the literature for such vector variational problems

Tangential Extremal Principles for Finite and Infinite Systems of Sets, II: Applications to Semi-infinite and Multiobjective Optimization

This paper contains selected applications of the new tangential extremal principles and related results developed in Part I to calculus rules for infinite intersections of sets and optimality conditions for problems of semi-infinite programming and multiobjective optimization with countable constraint

Sufficient optimality criteria and duality for multiobjective variational control problems with G-type I objective and constraint functions

In the paper, we introduce the concepts of G-type I and generalized G-type I functions for a new class of nonconvex multiobjective variational control problems. For such nonconvex vector optimization problems, we prove sufficient optimality conditions for weakly efficiency, efficiency and properly efficiency under assumptions that the functions constituting them are G-type I and/or generalized G-type I objective and constraint functions. Further, for the considered multiobjective variational control problem, its dual multiobjective variational control problem is given and several duality results are established under (generalized) G-type I objective and constraint functions

A Coevolutionary Particle Swarm Algorithm for Bi-Level Variational Inequalities: Applications to Competition in Highway Transportation Networks

A climate of increasing deregulation in traditional highway transportation, where the private sector has an expanded role in the provision of traditional transportation services, provides a background for practical policy issues to be investigated. One of the key issues of interest, and the focus of this chapter, would be the equilibrium decision variables offered by participants in this market. By assuming that the private sector participants play a Nash game, the above problem can be described as a Bi-Level Variational Inequality (BLVI). Our problem differs from the classical Cournot-Nash game because each and every player’s actions is constrained by another variational inequality describing the equilibrium route choice of users on the network. In this chapter, we discuss this BLVI and suggest a heuristic coevolutionary particle swarm algorithm for its resolution. Our proposed algorithm is subsequently tested on example problems drawn from the literature. The numerical experiments suggest that the proposed algorithm is a viable solution method for this problem

The proximal point method for locally lipschitz functions in multiobjective optimization with application to the compromise problem

This paper studies the constrained multiobjective optimization problem of finding Pareto critical points of vector-valued functions. The proximal point method considered by Bonnel, Iusem, and Svaiter [SIAM J. Optim., 15 (2005), pp. 953–970] is extended to locally Lipschitz functions in the finite dimensional multiobjective setting. To this end, a new (scalarization-free) approach for convergence analysis of the method is proposed where the first-order optimality condition of the scalarized problem is replaced by a necessary condition for weak Pareto points of a multiobjective problem. As a consequence, this has allowed us to consider the method without any assumption of convexity over the constraint sets that determine the vectorial improvement steps. This is very important for applications; for example, to extend to a dynamic setting the famous compromise problem in management sciences and game theory.Fundação de Amparo à Pesquisa do Estado de GoiásConselho Nacional de Desenvolvimento Científico e TecnológicoCoordenação de Aperfeiçoamento de Pessoal de Nivel SuperiorMinisterio de Economía y CompetitividadAgence nationale de la recherch