一类非凸约束优化问题的近似最优性条件及其混合型对偶

Approximate Optimality Conditions and Mixed Type Duality for a Class of Non-Convex Optimization Problems

利用函数Frechet次微分性质,引入新的约束规范条件,建立了目标函数和(或)约束函数为α-凸函数的非凸约束优化问题的近似最优性条件以及该问题及其混合型对偶问题之间的弱对偶、强对偶和逆对偶定理.

By using the properties of the Frechet subdifferentials,we first introduce a new constraint qualification and then establish some approximate optimality conditions for the nonconvex constrained optimization problem with objective function and/or constraint function beingα-convex function.Moreover,some results for the weak duality,strong duality and converse-like duality theorems between this non-convex optimization problem and its mixed type dual problem are also given.