G-ρ不变凸多目标规划的最优性条件

Optimality conditoins of G-ρinvex multi-objective programming

凸函数的推广在最优化理论中占有重要地位。利用局部Lipschitz函数,基于G-ρ不变凸函数、G-ρ不变拟凸函数和G-ρ不变伪凸函数,建立了含有不等式约束的多目标规划问题,证明了此函数凸性限制下的最优性充分条件,在更弱的凸性条件下推广了已有结论。

Convex function promotion plays an important role in optimisation theory.Using the local Lipschitz function,a multi-objective programming problem with inequality constraints was established based on the G-ρinvex func⁃tion,G-ρquasi-invex function and G-ρpseudo-invex function.The sufficient condition of optimality under the convexity constraint was proved,which extended the existing conclusions to the weaker convexity condition.