Improving the Performance of MIQP Solvers for Quadratic Programs with Cardinality and Minimum Threshold Constraints: A Semidefinite Program Approach
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- Xiaojin Zheng
- School of Economics and Management, Tongji University, Shanghai 200092, P. R. China
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- Xiaoling Sun
- Department of Management Science, School of Management, Fudan University, Shanghai 200433, P. R. China
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- Duan Li
- Department of Systems Engineering and Engineering Management, The Chinese University of Hong Kong, Shatin, N. T., Hong Kong
説明
<jats:p> We consider in this paper quadratic programming problems with cardinality and minimum threshold constraints that arise naturally in various real-world applications such as portfolio selection and subset selection in regression. This class of problems can be formulated as mixed-integer 0-1 quadratic programs. We propose a new semidefinite program (SDP) approach for computing the “best” diagonal decomposition that gives the tightest continuous relaxation of the perspective reformulation of the problem. We also give an alternative way of deriving the perspective reformulation by applying a special Lagrangian decomposition scheme to the diagonal decomposition of the problem. This derivation can be viewed as a “dual” method to the convexification method employing the perspective function on semicontinuous variables. Computational results show that the proposed SDP approach can be advantageous for improving the performance of mixed-integer quadratic programming solvers when applied to the perspective reformulations of the problem. </jats:p>
収録刊行物
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- INFORMS Journal on Computing
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INFORMS Journal on Computing 26 (4), 690-703, 2014-11
Institute for Operations Research and the Management Sciences (INFORMS)
