Cutting planes from the Boolean Quadric Polytope can be used to reduce the optimality gap of the NP-hard nonconvex quadratic program with box constraints (BoxQP). It is known that all cuts of the Chvátal–Gomory closure of the Boolean Quadric Polytope are A -odd cycle inequalities. We obtain a...

Methods are developed and analyzed for estimating the distance to a local minimizer of a nonlinear programming problem. One estimate, based on the solution of a constrained convex quadratic program, can be used when strict complementary slackness and the second-order sufficient optimality...

We introduce a new relaxation framework for nonconvex quadratically constrained quadratic programs (QCQPs). In contrast to existing relaxations based on semidefinite programming (SDP), our relaxations incorporate features of both SDP and second order cone programming (SOCP) and, as a result,...

In a real situation, optimization problems often involve uncertain parameters. Robust optimization is one of distribution-free methodologies based on worst-case analyses for handling such problems. In this paper, we first focus on a special class of uncertain linear programs (LPs). Applying the...