Exact Cutting Plane Methods for Quadratic Programming Problems with Applications

Abstract

This thesis bridges the methodological divide between concave and nonconcave optimisation by adapting cutting plane techniques to nonconcave mixed-integer quadratic programming problems. We introduce the novel concept of directional concavity, asserting the concavity of a quadratic function along specific directions, which enables the use of linear approximations for global optimization. This approach results in efficient exact methods for solving general quadratic programming problems.