Further Generalizations of Farkas' Theorem and Their Applications in Optimal Control☆☆☆
Further Generalizations of Farkas' Theorem and Their Applications in Optimal Control☆☆☆
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DOI：
10.1006/jmaa.1997.5612
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发表时间：
1997-12
影响因子：
1.3
通讯作者：
V. Phat;Jong Yeoul Park
中科院分区：
文献类型：
--
作者：
V. Phat;Jong Yeoul Park
本文讨论了无限维Banach空间中一类具有任意凸锥的集值映射的Farkas定理的一些新推广。给出了一个不带闭性假设的修正法卡斯定理。本文给出了非线性规划中的广义Gale替代定理。将所得结果应用于Banach空间的约束可控性理论以及一些多目标优化问题。
Abstract This paper deals with some new generalizations of Farkas' theorem for a class of set-valued mappings with arbitrary convex cones in infinite-dimensional Banach spaces. A modified Farkas' theorem with no closedness assumption is given. The generalized Gale alternative theorem in nonlinear programming is derived as an easy consequence. The results are applied to constrained controllability theory in Banach spaces as well as to some multiobjective optimization problem.