On Constrained Mixed-Integer DR-Submodular Minimization

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-04-08 DOI:10.1287/moor.2022.0320

Qimeng Yu, Simge Küçükyavuz

引用次数: 0

Abstract

Diminishing returns (DR)–submodular functions encompass a broad class of functions that are generally nonconvex and nonconcave. We study the problem of minimizing any DR-submodular function with continuous and general integer variables under box constraints and, possibly, additional monotonicity constraints. We propose valid linear inequalities for the epigraph of any DR-submodular function under the constraints. We further provide the complete convex hull of such an epigraph, which, surprisingly, turns out to be polyhedral. We propose a polynomial-time exact separation algorithm for our proposed valid inequalities with which we first establish the polynomial-time solvability of this class of mixed-integer nonlinear optimization problems.Funding: This work was supported by the Office of Naval Research Global [Grant N00014-22-1-2602].

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关于受约束混合整数 DR 次模态最小化

收益递减（DR）-次模态函数包括一大类函数，它们通常是非凸非凹的。我们研究的问题是，在盒式约束和可能的附加单调性约束下，如何最小化任何具有连续和一般整数变量的 DR 次模态函数。我们提出了约束条件下任何 DR 次模态函数外延的有效线性不等式。我们进一步提供了这样一个外延的完整凸壳，令人惊讶的是，这个凸壳竟然是多面体的。我们针对所提出的有效不等式提出了一种多项式时间精确分离算法，通过这种算法，我们首先建立了这一类混合整数非线性优化问题的多项式时间可解性：这项工作得到了全球海军研究办公室[N00014-22-1-2602 号拨款]的支持。

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

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.