Strong KKT Conditions For Nonsmooth Multiobjective Optimization Problems

Strong KKT conditions for multiobjective optimization problems are the KKT optimality conditions in which all the Lagrange multipliers corresponding to each component of the objective function are positive,and the strong KKT conditions are established under the assumption of certain constraint qualifi-cations.The study in constraint qualifications and the strong KKT conditions is an important research topic in the field of multiobjective optimization,and a series of important results have been achieved in this field.In this thesis,we consider a nonsmooth multiobjective optimization prob-lem with inequality constraints and an arbitrary set constraint,where the objective functions involved in the problem are locally Lipschitz.Two new generalized Abadie constraint qualifications are introduced by using the Clarke subdifferentials,contingent cones and Clarke tangent cones,and some new re-sults of strong KKT necessary optimality conditions for efficiency are obtained mainly by the strong separation theorem of convex set.Moreover,the relation-ships among the constraint qualifications proposed in this thesis and several other generalized Abadie constraint qualifications are studied.