Solution to nonconvex quadratic programming with both inequality and box constraints

Abstract

This paper presents a canonical dual approach for solving nonconvex quadratic programming problems subjected to both linear inequality constraints and box constrains. It is proved that the constrained nonconvex primal problem can be reformulated as a concave maximization dual problem with zero duality gap, which can be solved under certain conditions. Both global and local extremimality conditions are presented by the triality theory. Several applications are illustrated.