On the relationship between the integer and continuous solutions of convex programs

Authors:
X. L. Sun;D. Li
Affiliations:
Department of Mathematics, Shanghai University, Baoshan, Shanghai 200436, People's Republic of China;Department of Systems Engineering and Engineering Management, The Chinese University of Hong Kong, Shatin, N. T., Hong Kong
Venue:
Operations Research Letters
Year:
2001

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Abstract

A bound is obtained in this note for the distance between the integer and real solutions to convex quadratic programs. This bound is a function of the condition number of the Hessian matrix. We further extend this proximity result to convex programs and mixed-integer convex programs. We also show that this bound is achievable in certain situations and the distance between the integer and continuous minimizers may tend to infinity.