非凸半无限多目标规划近似解的最优性条件

Optimality Conditions for Approximate Solutions of Nonconvex Semi-infinite Multiobjective Programming

针对一类非凸半无限多目标规划问题,建立了其近似解的最优性条件。借助切向次微分定义了新的正则条件以及广义不变凸函数,值得注意的是,涉及的函数并不需要满足局部Lipschitz条件。首先,给出半无限多目标规划问题的(η,ε)-拟弱有效解和(η,ε)-拟有效解的定义,在正则条件的假设下,获得(η,ε)-拟弱有效解的必要最优性条件;然后,在广义不变凸性假设下,获得(η,ε)-拟(弱)有效解的充分最优性条件;所得结果推广和改进了相关文献的主要结论。

Optimality conditions of approximate solutions for nonconvex semi-infinite multiobjective programming problem are established.By means of tangential subdifferential,some new regular conditions and generalized invex functions are defined.It’s worth noting that the functions involved are not necessarily local Lipschitz.The definitions of(η,ε)-quasi weakly efficient solutions and(η,ε)-quasi efficient solutions for semi-infinite multiobjective programming problems are introduced.By the regular conditions,the necessary optimality condition of(η,ε)-quasi weakly efficient solutions is obtained.Moreover,the sufficient optimality condition of(η,ε)-quasi(weakly)efficient solutions is proposed by the generalized invex convexity.The results obtained in this paper improve and generalize the corresponding results in the literature.