The Optimality Conditions For Multiobjective Mathematical Programs With Conic Equilibrium Constraints

Multiobjective mathematical programs with conic equilibrium constraints are constrained optimization problems whose constraints include parameterized generalized equations or varia-tional inequalities. Many optimization problems can be formulated as the above multiobjective optimality problem with parameterized quasi-variational inequalities. For example, multiob-jective bilevel programming problems and multiobjective optimization problems with quasi-variational inequalities constraints, these are examples of this problem. In this paper, we will study the first-order optimality conditions of multiobjective optimality problems constrained by two special conic equilibrium constraints. The main results are summarized as follows:In the third chapter, we obtain the first-order optimality necessary conditions for multi-objective optimization problem constrained with quasi-variational inequalities constraints. The normal cone of constrained set with equalities and inequalities is obtained by means of normal cone to sets with constraints structure. Under the calmness conditions, an efficient upper esti-mate is also obtained to the normal cone of the constrain set with quasi-variational inequalities. Next, by separation theorem for convex sets, we change the multiobjective optimization problem into single-objective optimization problem and then we get the first-order optimality necessary conditions for multiobjective optimization problem.In the fourth chapter, we obtain the first-order optimality necessary conditions for multiob-jective optimization problem governed by second-order cone constrained generalized equations. The nonnal cone of constrained set with second-order cone is obtained by means of normal cone to sets with constraints structure. Under the calmness conditions, an efficient upper estimate of coderivative for a composite set-valued mapping is derived, which is also obtained to the nor-mal cone of the constrain set with second-order cone. At last we get the first-order optimality conditions for multiobjective optimization problem.