向量优化ε-严有效解的非线性标量化刻画

Nonlinear scalarization characterizations for strictly efficient solutions of vector optimization

在局部凸Hausdorff拓扑向量空间中研究了向量优化逼近严有效解的非线性标量化问题。研究了逼近锥及其内部的性质,利用Gpfert等提出的非线性标量化函数分别给出了向量优化逼近严有效解的充分和必要条件,并举例说明了主要结果。

The nonlinear scalarization problem for approximate strictly efficient solutions of vector optimization is considered in locally convex topological spaces.Properties for approximate cones and their interiors are discussed,by applying the nonlinear scalarization functions proposed by Gpfert et al.,sufficient and necessary optimality conditions are established for approximate strictly efficient solutions of vector optimization,respectively,and an example is given to illustrate the main result.