线性空间中集值映射向量优化问题的ε-真有效解

ε-Properly Efficient Solutions of Vector Optimization Problems with Set-Valued Maps in Linear Spaces

利用一种称为代数型闭包的向量闭包,讨论了线性空间中极值映射向量优化问题的ε-真有效解,在集值映射为广义向量似凸的假设下,建立了这种解的标量化定理和ε-Lagrange乘子定理.

The authors use a concept of algebraic type of closure which is called vector closure . Through this closure they discuss ε-properly efficient solutions of vector optimization problems with set-valued maps. Under the assumption of the generalized cone-subconvexlikeness for Set-valued maps, the authors obtain the scalarization theorem and the ε-Lagrange multipliers theorems for ε-properly efficient solutions of vector optimization problems with set-valued maps.