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Submodular Minimization in the Context of Modern LP and MILP Methods and Solvers

机译：现代LP和MILP方法和求解器背景下的子模块最小化

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摘要

We consider the application of mixed-integer linear programming (MILP) solvers to the minimization of submodular functions. We evaluate common large-scale linear-programming (LP) techniques (e.g., column generation, row generation, dual stabilization) for solving a LP reformulation of the submodular minimization (SM) problem. We present heuristics based on the LP framework and a MILP solver. We evaluated the performance of our methods on a test bed of min-cut and matroid-intersection problems formulated as SM problems.

机译：我们考虑将混合整数线性编程（MILP）求解器的应用应用于最小化子模块功能。我们评估常见的大规模线性编程（LP）技术（例如，列生成，行产生，双稳定），用于求解子骨髓最小化（SM）问题的LP重构。我们呈现基于LP框架和MILP求解器的启发式。我们评估了我们在敏捷和麦克风 - 交叉点问题的试验台上表现为SM问题的表现。

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《International Symposium on Experimental Algorithms 》|2015年||共12页
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作者
Andrew Orso; Jon Lee; Siqian Shen;
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正文语种
中图分类 TP301-53;
关键词
Submodular minimization; Lovasz extension; Column generation; Row generation; Dual stabilization;

机译：子模具最小化;Lovasz延伸;列生成;行生成;双重稳定;

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2. Stochastic Conditional Gradient Methods: From Convex Minimization to Submodular Maximization [J] . Aryan Mokhtari, Hamed Hassani, Amin Karbasi Journal of machine learning research . 2020 ,第a期

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4. Submodular Minimization in the Context of Modern LP and MILP Methods and Solvers [C] . Andrew Orso, Jon Lee, Siqian Shen International symposium on experimental algorithms . 2015

机译：现代LP和MILP方法和求解器背景下的亚模最小化
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Submodular Minimization in the Context of Modern LP and MILP Methods and Solvers

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