Optimality Conditions For Vector Bilevel Optimization Problems And Error Bounds For Vector Equilibrium Problems

In this thesis, we study two problems: the optimality conditions for vector bilevel optimization problems and the error bounds for vector equilibrium problems. The detailed contents are listed as following:First, the thesis is concerned with the optimistic formulation of a bilevel optimization problem with multiobjective lower-level problem. Unless of convex assumption, we transform the lower-level problem into a scalar-objective optimization by the Gerstewitz function which is a nonlinear scalarization function. Then by the optimal value reformulation, one level scalari-objective optimization is obtained which is equivalent to the original problem. Finally, necessary optimality conditions for the vector bilevel optimization are derived while using the generalized differentiation calculus of Mordukhovich.Secondly, we intend to study the vector equilibrium problems. Without any scalarization approach, the gap functions and their regularized versions for vector equilibrium problems are obtained. Under mild conditions, we develop an error bounds for vector equilibrium problems with strongly monotone data. As an application, we also get the gap functions and error bounds for the vector variational inequalities.