非光滑多目标优化问题中KT乘子集的非空有界性

Nonemptiness and Boundedness of Set of Kuhn-Tucker Multipliers in Nonsmooth Multiobjective Optimization

运用次微分convexificator提出约束规格并研究具有不等式和集合约束的局部Lipschitz多目标优化问题KT乘子集的非空有界性,得到了在局部弱有效解处所提出的约束规格是KT乘子集非空有界的充分必要条件.

Using the idea of convexificators, we proposed constraint qualifications and studied the existence and boundedness of the Kuhn-Tucker multipliers for a nonsmooth muhiobjective optimization problem with inequality constraints and an arbitrary set constraint. We showed that in locally weak efficient solutions where the objective and constraint functions are locally Lipschitz, the constraint qualifications are necessary and sufficient conditions for the Kuhn-Tucker multiplier Sets to be nonempty and bounded.