一类多目标优化问题弱有效解的必要最优性条件

Necessary Optimality Conditions for a Class of Nonsmooth Constrained Multiobjective Optimization Problems

标量化方法是研究多目标优化问题的最优性条件与算法的重要手段,最优性理论是优化理论的重要研究内容之一.建立了一类标量化函数的相关性质,并借助标量化技巧与Clarke次微分,在假设次微分约束规格成立的条件下,建立了一类非光滑多目标优化问题的局部弱有效解的Karush-Kuhn-Tucker必要最优性条件.

The scalarization method is an important means for the study of optimality and algorithms of multi-objective optimization problems,and optimality theory is one of the important contents in the optimization theory.In this paper,we first establish some properties of a class of scalarization functions.Then,with the scalarization method and Clarke subdifferentials,we establish the Karush-Kuhn-Tucker necessary optimality conditions for the local weakly efficient solution of a nonsmooth constrained multi-objective optimization problem under the assumption of subdifferential constraint qualification.