非光滑多目标优化鲁棒近似解的最优性和鞍点定理

Optimality and saddle point theorem for robust approximation solutions for non-smooth multi-objective optimization

借助强凸函数,定义了广义强伪拟凸函数,并在广义强凸性和Slater约束的假设条件下,研究了具有不确定参数的非光滑多目标优化问题,给出多目标优化问题可行解成为鲁棒(弱)有效解和鲁棒ε-拟弱有效解的最优性充分条件;建立鞍点定理,得到了弱鞍点与原优化ε-拟弱有效解的等价性。在更弱的广义凸性下推广了多目标鲁棒优化问题的最优性条件和鞍点条件。

With the help of strong convex functions,a generalized strong pseudo-quasi-convex function is defined.Under the assumptions of generalized strong convexity and Slater constraints,non-smooth multi-objective optimization problems with uncertain parameters are studied,and feasible solutions to the optimality multi-objective optimization problem to become a robust(weak)sufficient condition and a robustε-quasi-weak efficient solution are given.By establishing the saddle point theorem,the equivalence between the weak saddle points and the original optimizedε-quasi-weak effective solution is obtained.The optimality condition and saddle point condition of multi-objective robust optimization problem are generalized under the weaker generalized convexity.