On zero duality gap in nonconvex quadratic programming 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;Department of Management Science, School of Management, Fudan University, Shanghai, People's Republic of China 200433;Department of Systems Engineering and Engineering Management, The Chinese University of Hong Kong, Shatin, Hong Kong;Department of Management Science, School of Management, Fudan University, Shanghai, People's Republic of China 200433
Venue:
Journal of Global Optimization
Year:
2012

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Abstract

We present in this paper new sufficient conditions for verifying zero duality gap in nonconvex quadratically/linearly constrained quadratic programs (QP). Based on saddle point condition and conic duality theorem, we first derive a sufficient condition for the zero duality gap between a quadratically constrained QP and its Lagrangian dual or SDP relaxation. We then use a distance measure to characterize the duality gap for nonconvex QP with linear constraints. We show that this distance can be computed via cell enumeration technique in discrete geometry. Finally, we revisit two sufficient optimality conditions in the literature for two classes of nonconvex QPs and show that these conditions actually imply zero duality gap.