集值约束的多目标线性优化问题的弱对偶定理

Weak duality theorem about multi-objective linear vector optimization with set-valued constraint

对偶理论是数学规划的理论基础,其中在各种约束条件下对弱对偶定理的研究是对偶理论研究的重要组成部分。应用集值对偶理论证明了集值约束的线性优化问题的弱对偶定理,得到了与单值约束的线性向量优化问题的弱对偶定理和强对偶定理相似的结论,并且证明了与弱对偶定理等价的几个式子,从而推广和完善了对偶理论。

The duality theory is the basic theory for mathematical planning in which the study of weak duality theorem under different controlling conditions is an important part of duality theorem research. Document [2] discusses the weak duality theorem and the strong duality theorem of linear vector optimization with single value constraint. With the set-value duality theory, this paper demonstrates the weak duality theorem of linear vector optimization with set-valued constraint and reaches the similar conclusion with that in document [2]. At the same time it proves a few formulae which are equal to the weak duality theorem.Thus we generalized and completed the duality theory.