On reduction of duality gap in quadratic knapsack problems

Authors:
X. J. Zheng;X. L. Sun;D. Li;Y. F. Xu
Affiliations:
Department of Management Science, School of Management, Fudan University, Shanghai, People's Republic of China 200433;School of Economics and Management, Tongji University, Shanghai, People's Republic of China 200092;Department of Systems Engineering and Engineering Management, The Chinese University of Hong Kong, Shatin, Hong Kong;School of Economics and Management, Tongji University, Shanghai, People's Republic of China 200092
Venue:
Journal of Global Optimization
Year:
2012

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Abstract

We investigate in this paper the duality gap between quadratic knapsack problem and its Lagrangian dual or semidefinite programming relaxation. We characterize the duality gap by a distance measure from set {0, 1} n to certain polyhedral set and demonstrate that the duality gap can be reduced by an amount proportional to the square of the distance. We further discuss how to compute the distance measure via cell enumeration method and to derive the corresponding improved upper bound of the problem.