Lifted Polymatroid Inequalities for Mean-Risk Optimization with Indicator Variables
Abstract: We investigate a mixed 0-1 conic quadratic optimization problem with indicator variables arising in mean-risk optimization. The indicator variables are often used to model non-convexities such as fixed charges or cardinality constraints. Observing that the problem reduces to a submodular function minimization for its binary restriction, we derive three classes of strong convex valid inequalities by lifting the polymatroid inequalities on the binary variables. Computational experiments demonstrate the effectiveness of the inequalities in strengthening the convex relaxations and, thereby, improving the solution times for mean-risk problems with fixed charges and cardinality constraints significantly.
Keywords: Risk, submodularity, polymatroid, conic integer optimization, valid inequalities.
Category 1: Integer Programming ((Mixed) Integer Nonlinear Programming )
Category 2: Stochastic Programming
Citation: BCOL Research Report 17.01, University of California, Berkeley
Entry Submitted: 04/07/2017
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