一类两阶段自适应鲁棒多目标规划的对偶性刻画

Duality Characterizations for a Class of Two-Stage Adjustable Robust Multiobjective Programming

该文主要研究一类目标函数和约束函数均具有谱面不确定数据的两阶段自适应鲁棒多目标规划问题.首先,建立具有仿射自适应变量的两阶段自适应鲁棒多目标规划问题的Farkas引理.随后,引入该多目标规划问题的半定规划对偶问题.最后,借助该Farkas引理,刻画它们之间的对偶性质.

In this paper,we deal with a class of two-stage adjustable robust multi-objective program-ming problems with spectrahedral uncertainty data in both objective and constraints.We first establish a Farkas lemma for a two-stage adjustable robust multiobjective programming with affine adjustable variable,Then,we propose a semidefinite programming dual problem for this multiobjective program-ming problem.Furthermore,in terms of the obtained Farkas lemma,we explore duality properties between them.