Virginia TechFang, S. C.Gao, D. Y.Sheu, R. L.Wu, S. Y.2014-05-142014-05-142008-02Fang, S. C.; Gao, D. Y.; Sheu, R. L.; Wu, S. Y., "Canonical dual approach to solving 0-1 quadratic programming problems," J. Industrial and Management Optimization 4(1), 125-142, (2008); DOI: 10.3934/jimo.2008.4.1251547-5816http://hdl.handle.net/10919/47975This 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.en-USIn Copyrightglobal optimizationdualitynonconvex minimizationbox constraintsinteger programmingboolean least squares problemnp-hard problemsglobal optimizationconvex underestimatorstriality theoryduality-theoryengineering, multidisciplinaryoperations research & managementsciencemathematics, interdisciplinary applicationsArticle - Refereedhttp://www.aimsciences.org/journals/displayArticles.jsp?paperID=3089https://doi.org/10.3934/jimo.2008.4.125