向量优化问题E-有效解的非线性标量化刻画

Nonlinear Scalarization Characterizations of E-Efficient Solution of Vector Optimization Problem

利用基于改进集E的Gerstewitz泛函φ及面向距离函数Δ等两类非线性标量化函数对向量优化问题的E-有效解、E-弱有效解及E-严有效解等有效解进行刻画,并给出相应例子对部分结论进行说明。

Characterizations for the E-efficient solution,E-weak efficient solution and E-strictly efficient solution of vector optimization problems are established by two types of nonlinear scalarization function called the Gerstewitz functionalφand the oriented distance functionΔvia improvement sets.Some corresponding examples are constructed to illustrate the conclusions.