On Constrained Mixed-Integer DR-Submodular Minimization

Qimeng Yu; Simge Küçükyavuz

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arXiv · 2211.07726

On Constrained Mixed-Integer DR-Submodular Minimization

Qimeng Yu·Simge Küçükyavuz

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Abstract

DR-submodular functions encompass a broad class of functions which are generally non-convex and non-concave. 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.

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BibTeX RIS

Qimeng Yu, Simge Küçükyavuz. 2022-11-14. On Constrained Mixed-Integer DR-Submodular Minimization. https://arxiv.org/abs/2211.07726

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