无限指标集上的择一定理及其在向量优化中的应用

Alternative Theorem on Infinite Index Set and Its Application in Vector Optimization

【目的】探究无限多个准则的向量优化问题解的刻画。【方法】通过建立无限指标集上的择一定理,研究了无限多个准则的向量优化问题的弱有效解、有效解和G-真有效解的标量化刻画。【结果】首先,在不需要任何凸性条件下建立了无限指标集上的择一定理。随后,将择一定理应用到无限多个准则的向量优化问题中,给出了弱有效解、有效解和G-真有效解的标量化结果。【结论】所得结果对处理无限多个准则的向量优化问题具有实际意义。

[Purposes]Exploring the characterization description of the solution to the vector optimization problem with infinite multiple criteria.[Methods]Establishing an alternative theorem on an infinite index set,studying the characterization of weak efficient solution,efficient solution and G-proper efficient solution of the vector optimization problem with infinite multiple criteria.[Findings]First of all,the alternative theorem on the infinite index set is established without any convexity.Subsequently,the alternative theorem is applied to the vector optimization problem of infinite multiple criteria,and the scalarized results for the weak efficient solution,the efficient solution and G-proper efficient solution are given.[Conclusions]It has practical significance for dealing with vector optimization problems with infinite multiple criteria.