论文标题
基于提升和项目的圆锥线性优化的多参数分析
Multiparametric analysis of conic linear optimization based on the lift-and-project procedure
论文作者
论文摘要
我们研究了提升和项目如何应用于圆锥线性优化（CLO）问题的多参数分析。我们首先介绍了一对原始和双锥形代表集的概念，并定义了它们之间的设置值映射。然后，我们探索了MPCLOS的一种新颖的双重性，它使我们能够在统一框架中概括并治疗MulitParametric Analysis的先前结果。特别是，我们讨论了锥形代表集的最佳分区的行为。这导致可代表圆锥体的集合的不变区域分解，该集合比文献中的已知结果更一般。最后，我们研究最佳目标值的特性是该参数向量的函数。所有结果都通过相关示例来证实。
We study how the lift-and-project procedure applies to the multiparametric analysis of conic linear optimization (CLO) problems. We first introduce the concept of a pair of primal and dual conic representable sets and define the set-valued mappings between them. We then explore a novel kind of duality of mpCLOs, which allows us to generalize as well as treat previous results for the mulitparametric analysis in a unified framework. In particular, we discuss the behavior of the optimal partition of a conic representable set. This leads to the invariant region decomposition of a conic representable set that is more general than the known results in the literatures. Finally, we study the properties of the optimal objective values as a function of that parametric vectors. All results are corroborated by examples having correlation.
