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

Andrew Orso(orso***at***umich.edu)
Jon Lee(jonxlee***at***umich.edu)
Siqian Shen(siqian***at***umich.edu)

Abstract: 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.

Keywords: submodular minimization, Lovasz extension, column generation, row generation, dual stabilization

Category 1: Combinatorial Optimization

Category 2: Linear, Cone and Semidefinite Programming (Linear Programming )

Category 3: Integer Programming (0-1 Programming )

Citation:

Download: [PDF]

Entry Submitted: 01/30/2015
Entry Accepted: 02/01/2015
Entry Last Modified: 01/30/2015

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