The Distributions of Functions Related to Parametric Integer Optimization

IF 1.6 2区 数学 Q2 MATHEMATICS, APPLIED
Timm Oertel, Joseph Paat, R. Weismantel
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引用次数: 16

Abstract

We consider the asymptotic distribution of the IP sparsity function, which measures the minimal support of optimal IP solutions, and the IP to LP distance function, which measures the distance between optimal IP and LP solutions. To this end, we create a framework for studying the asymptotic distribution of general functions related to integer optimization. While there has been a significant amount of research focused around the extreme values that these functions can attain, little is known about their typical values. Each of these functions is defined for a fixed constraint matrix and objective vector while the right hand sides are treated as input. We show that the typical values of these functions are smaller than the known worst case bounds by providing a spectrum of probability-like results that govern their overall asymptotic distributions.
参数整数优化相关函数的分布
我们考虑了IP稀疏度函数的渐近分布,它测量了最优IP解的最小支持度,以及IP到LP距离函数,它测量了最优IP和LP解之间的距离。为此,我们创建了一个研究与整数优化相关的一般函数的渐近分布的框架。虽然已经有大量的研究集中在这些功能可以达到的极端值上,但对它们的典型值知之甚少。每个函数都定义为一个固定的约束矩阵和目标向量,而右手边被视为输入。我们通过提供控制其整体渐近分布的类概率结果的谱来证明这些函数的典型值小于已知的最坏情况边界。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
CiteScore
2.20
自引率
0.00%
发文量
19
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