不等式约束的广义拟可微优化问题最优性条件

Optimality conditions for generalized quasi-differentiable optimization problems with inequality constraints

B racken-M cG ill双层规划问题和其他某些重要的不可微优化问题均是广义拟可微优化问题,这类问题的最优性条件的研究是非常重要的.为此提出了一个关于一类正齐次函数的F arkas引理,基于这一引理,在一约束规范之下,建立了不等式约束的广义拟可微优化问题的最优性条件,并证明约束规范是一个正则条件的充分条件.

The study of optimality conditions for generalized quasi-differentiable optimization is very important for Bracken-McGill bilevel programming and other important nondifferentiable optimization problems. Based on a Farkas lemma of a class of positively homogeneous functions proposed in this paper, a set of necessary conditions, under a constraint qualification, for a local minimizer to a generalized quasi-differentiable optimization problem, is demonstrated. It is also shown that the constraint qualification used in optimality conditions implies a regular condition.