Local search and swapping strategies.Challenging the greedy maximization of a polymatroid subject to a cardinality constraint

This paper studies the maximization of a polymatroid subject to a cardinality constraint. In particular, we consider the problem of improving the value of the greedy set by swapping one of its members with an element that does not belong to it. To achieve this goal, we first define a (set-based) post-greedy measure of curvature … Read more

Submodularity in conic quadratic mixed 0-1 optimization

We describe strong convex valid inequalities for conic quadratic mixed 0-1 optimization. These inequalities can be utilized for solving numerous practical nonlinear discrete optimization problems from value-at-risk minimization to queueing system design, from robust interdiction to assortment optimization through appropriate conic quadratic mixed 0-1 relaxations. The inequalities exploit the submodularity of the binary restrictions and … Read more

Lifted Polymatroid Inequalities for Mean-Risk Optimization with Indicator Variables

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 … Read more