Enhancements of Discretization Approaches for Non-Convex Mixed-Integer Quadratically Constraint Quadratic Programming: Part II

Abstract. This is Part II of a study on mixed-integer programming (MIP) relaxation techniques for the solution of non-convex mixed-integer quadratically constrained quadratic programs (MIQCQPs). We set the focus on MIP relaxation methods for non-convex continuous variable products and extend the well-known MIP relaxation normalized multiparametric disaggregation technique (NMDT), applying a sophisticated discretization to both … Read more

Enhancements of Discretization Approaches for Non-Convex Mixed-Integer Quadratically Constraint Quadratic Programming: Part I

We study mixed-integer programming (MIP) relaxation techniques for the solution of non-convex mixed-integer quadratically constrained quadratic programs (MIQCQPs). We present MIP relaxation methods for non-convex continuous variable products. In Part I, we consider MIP relaxations based on separable reformulation. The main focus is the introduction of the enhanced separable MIP relaxation for non-convex quadratic products … Read more

Compact mixed-integer programming relaxations in quadratic optimization

We present a technique for producing valid dual bounds for nonconvex quadratic optimization problems. The approach leverages an elegant piecewise linear approximation for univariate quadratic functions due to Yarotsky, formulating this (simple) approximation using mixed-integer programming (MIP). Notably, the number of constraints, binary variables, and auxiliary continuous variables used in this formulation grows logarithmically in … Read more