Solutions and optimality criteria to box constrained nonconvex minimization problems

Abstract

This paper presents a canonical duality theory for solvingnonconvex polynomial programming problems subjected to boxconstraints. It is proved that under certain conditions, the constrained nonconvex problems can be converted to the so-called canonical (perfect) dual problems, which can be solved by deterministic methods.Both global and local extrema of the primal problems can be identified by a triality theory proposed by the author. Applications to nonconvex integer programming and Boolean least squares problems are discussed. Examples are illustrated. A conjecture on NP-hard problems is proposed.