集值优化问题广义近似解的线性标量化

Nonlinear Scalarization Theorems of Generalized Approximate Solutions in Set-valued Optimization Problems

【目的】对广义近似(弱)有效解的性质作进一步研究。【方法】利用线性标量化方法研究了集值优化问题广义近似(弱)有效解的刻画。【结果】建立了广义次似凸条件下的择一性定理,给出了广义弱近似解的一个标量化定理,并进一步研究了广义近似解(弱)有效解的一些性质。【结论】将集值函数F是凸的推广到次似凸的情形,并进一步完善了广义近似解的一些性质。

[Purposes]The properties of generalized approximate （weakly） efficient solutions are mainly studied here. [Methods]The characterization of generalized approximate （weak） efficient solutions for set-valued optimization problems using linear scalar method. [Findings]The alternative theorem of generalized sub convex like condition is established, and the sealarization theorerns of generalized weak approximate solutions is given, and some properties of the generalized approximate （weak） efficient solution are further studied, [Conclusions]The generalization of set-valued function F is convex to sub convex, and some properties of generalized approximate solutions are further improved.