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We study mixed-integer programming (MIP) relaxation techniques for thesolution of non convex mixed-integer quadratically constrained quadraticprograms (MIQCQPs). We present MIP relaxation methods for non convex continuousvariable products. In Part I, we consider MIP relaxations based on separablereformulation. The main focus is the introduction of the enhanced separable MIPrelaxation for nonconvex quadratic products of the form z=xy, called hybridseparable (HybS). Additionally, we introduce a logarithmic MIP relaxation forunivariate quadratic terms, called sawtooth relaxation. We combine the latterwith HybS and existing separable reformulations to derive MIP relaxations ofMIQCQPs. We provide a comprehensive theoretical analysis of these techniques,underlining the theoretical advantages of HybS compared to its predecessors. Weperform a broad computational study to demonstrate the effectiveness of theenhanced MIP relaxation in terms of producing tight dual bounds for MIQCQPs. InPart II, we study MIP relaxations that extend the well-known MIP relaxationnormalized multiparametric disaggregation technique (NMDT) and present furthertheoretical and computational analyses.

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