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January  2008, 4(1): 125-142. doi: 10.3934/jimo.2008.4.125

Canonical dual approach to solving 0-1 quadratic programming problems

Shu-Cherng Fang 1, , David Y. Gao 2, , Ruey-Lin Sheu 3, and  Soon-Yi Wu 4,

1. 

Department of Industrial and Systems Engineering, North Carolina State University, Raleigh, NC, United States
2. 

Department of Mathematics, Virginia Tech, Blacksburgh, VA, United States
3. 

Department of Mathematics, National Cheng Kung University, Taiwan, ROC, Taiwan
4. 

Department of Mathematics, National Cheng Kung University, Tainan, Taiwan

Received  February 2007 Revised  November 2007 Published  January 2008

By using the canonical dual transformation developed recently, we derive a pair of canonical dual problems for 0-1 quadratic programming problems in both minimization and maximization form. Regardless convexity, when the canonical duals are solvable, no duality gap exists between the primal and corresponding dual problems. Both global and local optimality conditions are given. An algorithm is presented for finding global minimizers, even when the primal objective function is not convex. Examples are included to illustrate this new approach.
Keywords: integer programming, NP-hard problems., duality, global optimization, $0$-$1$ quadratic programming.
Mathematics Subject Classification: 49N15, 49M37, 90C26, 90C2.
Citation: Shu-Cherng Fang, David Y. Gao, Ruey-Lin Sheu, Soon-Yi Wu. Canonical dual approach to solving 0-1 quadratic programming problems. Journal of Industrial and Management Optimization, 2008, 4 (1) : 125-142. doi: 10.3934/jimo.2008.4.125
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