# American Institute of Mathematical Sciences

October  2010, 6(4): 779-793. doi: 10.3934/jimo.2010.6.779

## Extended canonical duality and conic programming for solving 0-1 quadratic programming problems

 1 Department of Mathematical Sciences, Tsinghua University, Beijing, China 2 Department of Industrial and System Engineering, North Carolina State University, Raleigh, NC 27695, United States

Received  February 2010 Revised  April 2010 Published  September 2010

An extended canonical dual approach for solving 0-1 quadratic programming problems is introduced. We derive the relationship between the optimal solutions to the extended canonical dual problem and the original problem and prove that there exists no duality gap in-between. The extended canonical dual approach leads to a sufficient condition for global optimality, which is more general than known results of this kind. To solve the extended canonical dual problem, we construct corresponding conic programming problems and study their relationship to the extended canonical dual problem. Using this relationship, we design an algorithm for solving the extended canonical dual problem. Our work extends the known solvable sub-class of 0-1 quadratic programming problems.
Citation: Cheng Lu, Zhenbo Wang, Wenxun Xing, Shu-Cherng Fang. Extended canonical duality and conic programming for solving 0-1 quadratic programming problems. Journal of Industrial & Management Optimization, 2010, 6 (4) : 779-793. doi: 10.3934/jimo.2010.6.779
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