Robust Mixed 0-1 Programming and Submodularity

Strong Formulations of Robust Mixed 0-1 Programming

We introduce strong formulations for robust mixed 0–1 programming with uncertain objective coefficients. We focus on a polytopic uncertainty set described by a “budget constraint” for allowed uncertainty in the objective coefficients. We show that for a robust 0–1 problem, there is an α–tight linear programming formulation with size polynomial in the size of an α–tight linear programming formul...

Submodularity in Conic Quadratic Mixed 0-1 Optimization

We describe strong convex valid inequalities for conic quadratic mixed 0-1 optimization. The inequalities exploit the submodularity of the binary restrictions and are based on the polymatroid inequalities over binaries for the diagonal case. We prove that the convex inequalities completely describe the convex hull of a single conic quadratic constraint as well as the rotated cone constraint ove...

Lift-and-project for Mixed 0-1 programming: recent progress

Proximity search for 0-1 mixed-integer convex programming

In this paper we investigate the effects of replacing the objective function of a 0-1 Mixed-Integer Convex Program (MIP) with a “proximity” one, with the aim of enhancing the heuristic behavior of a black-box solver. The relationship of this approach with primal integer methods is also addressed. Promising computational results on different proof-of-concept implementations are presented, sugges...

Heuristiques hybrides pour la résolution de problèmes en variables 0-1 mixtes. (Hybrid heuristics for 0-1 mixed integer programming)