Lower bounds for Chvátal-Gomory style operators

Valid inequalities or cutting planes for (mixed-) integer programming problems are an essential theoretical tool for studying combinatorial properties of polyhedra. They are also of utmost importance for solving optimization problems in practice; in fact any modern solver relies on several families of cutting planes. The Chvátal-Gomory procedure, one such approach, has a peculiarity that … Read more

Strong Branching Inequalities for Convex Mixed Integer Nonlinear Programs

Strong branching is an effective branching technique that can significantly reduce the size of the branch-and-bound tree for solving Mixed Integer Nonlinear Programming (MINLP) problems. The focus of this paper is to demonstrate how to effectively use discarded information from strong branching to strengthen relaxations of MINLP problems. Valid inequalities such as branching-based linearizations, various … Read more

Adjoint Sensitivity Analysis for Numerical Weather Prediction: Applications to Power Grid Optimization

We present an approach to estimate adjoint sensitivities of economic metrics of relevance in the power grid with respect to physical weather variables using numerical weather prediction models. We demonstrate that this capability can significantly enhance planning and operations. We illustrate the method using a large-scale computational study where we compute sensitivities of the regional … Read more

Facets for the Maximum Common Induced Subgraph Problem Polytope

This paper presents some strong valid inequalities for the Maximum Common Induced Subgraph Problem (MCIS) and the proofs that the inequalities are facet-defining under certain conditions. The MCIS is an NP-hard problem and, therefore, no polynomial time algorithm is known to solve it. In this context, the study of its polytope can help in the … Read more

Trajectory-following methods for large-scale degenerate convex quadratic programming

We consider a class of infeasible, path-following methods for convex quadratric programming. Our methods are designed to be effective for solving both nondegerate and degenerate problems, where degeneracy is understood to mean the failure of strict complementarity at a solution. Global convergence and a polynomial bound on the number of iterations required is given. An … Read more

A comparison of routing sets for robust network design

Designing a network able to route a set of non-simultaneous demand vectors is an important problem arising in telecommunications. The problem can be seen a two-stage robust program where the recourse function consists in choosing the routing for each demand vector. Allowing the routing to change arbitrarily as the demand varies yields a very difficult … Read more