American Institute of Mathematical Sciences

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April  2007, 3(2): 293-304. doi: 10.3934/jimo.2007.3.293

Solutions and optimality criteria to box constrained nonconvex minimization problems

David Yang Gao 1,

1. 

Department of Mathematics & Grado, Department of Industrial and System Engineering, Virginia Polytechnic Institute and State University, Blacksburg, VA, 24061, United States

Received  August 2006 Revised  January 2007 Published  April 2007

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.
Keywords: NP-hard problems., Global optimization; Duality; Nonconvex minimization; Box constraints; Integer programming; Boolean least squares problem.
Mathematics Subject Classification: 49N15, 49M37, 90C26, 90C2.
Citation: David Yang Gao. Solutions and optimality criteria to box constrained nonconvex minimization problems. Journal of Industrial & Management Optimization, 2007, 3 (2) : 293-304. doi: 10.3934/jimo.2007.3.293
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