一类集值映射向量优化问题的ε-有效解

ε-Efficient Solutions of A Class of Vector Optimization Problems with Set-Valued Maps

集值映射向量优化问题是最优化理论中的一个重要方向.在集值映射为生成锥内部-锥一类凸(简记为ic-锥类凸)的假设条件下,利用择一定理,给出了集值映射向量优化问题ε-弱有效解和ε-有效解的最优性条件和ε-Lagrange乘子定理,是弱有效解和有效解相应结果的推广.

Vector optimization problems with set-valued maps are important issues in the optimization theory. In this paper, we deal with vector optimization problem with ic-cone- convexlike set-valued maps. By using the alternative theorem, we obtain the necessary condi- tions and ε-Lagrange multiplier theorems for E-weakly efficient solution and ε-efficient solution for a class of vector optimization problems. Our results are the generalization of the corre- sponding results about weakly efficient solutian and efficient solution.