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Submodularity and valid inequalities in nonlinear optimization with indicator variables

Andres Gomez(agomez***at***pitt.edu)

Abstract: We propose a new class of valid inequalities for mixed-integer nonlinear optimization problems with indicator variables. The inequalities are obtained by lifting polymatroid inequalities in the space of the 01 variables into conic inequalities in the original space of variables. The proposed inequalities are shown to describe the convex hull of the set under study under appropriate submodularity conditions. Moreover, the inequalities include the perspective reformulation and pairwise inequalities for quadratic optimization with indicator variables as special cases. Finally, we use the proposed methodology to derive ideal formulations of other mixed-integer sets with indicator variables.

Keywords: Submodularity, Indicator variables, Mixed-integer optimization, Valid inequalities

Category 1: Integer Programming ((Mixed) Integer Nonlinear Programming )

Category 2: Integer Programming (Cutting Plane Approaches )

Citation: Research report AG 18.06, IE, University of Pittsburgh, November 2018

Download: [PDF]

Entry Submitted: 11/14/2018
Entry Accepted: 11/14/2018
Entry Last Modified: 11/14/2018

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