Gao, David Yang Solutions and optimality criteria to box constrained nonconvex minimization problems. (English) Zbl 1171.90504 J. Ind. Manag. Optim. 3, No. 2, 293-304 (2007). Summary: This paper presents a canonical duality theory for solving nonconvex polynomial programming problems subjected to box constraints. 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. Cited in 30 Documents MSC: 90C26 Nonconvex programming, global optimization 49N15 Duality theory (optimization) 49M37 Numerical methods based on nonlinear programming 90C20 Quadratic programming Keywords:global optimization; duality; integer programming; Boolean least squares problem; NP-hard problems PDF BibTeX XML Cite \textit{D. Y. Gao}, J. Ind. Manag. Optim. 3, No. 2, 293--304 (2007; Zbl 1171.90504) Full Text: DOI OpenURL