New reformulations for probabilistically constrained quadratic programs |
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| Authors: | Yong Hsia Baiyi Wu Duan Li |
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| Institution: | 1. State Key Laboratory of Software Development Environment, LMIB of the Ministry of Education, School of Mathematics and System Sciences, Beihang University, Beijing 100191, PR China;2. Department of Systems Engineering and Engineering Management, The Chinese University of Hong Kong, Shatin, NT, Hong Kong |
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| Abstract: | The mixed integer quadratic programming (MIQP) reformulation by Zheng, Sun, Li, and Cui (2012) for probabilistically constrained quadratic programs (PCQP) recently published in EJOR significantly dominates the standard MIQP formulation ( and ) which has been widely adopted in the literature. Stimulated by the dimensionality problem which Zheng et al. (2012) acknowledge themselves for their reformulations, we study further the characteristics of PCQP and develop new MIQP reformulations for PCQP with fewer variables and constraints. The results from numerical tests demonstrate that our reformulations clearly outperform the state-of-the-art MIQP in Zheng et al. (2012). |
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| Keywords: | Quadratic programming Probabilistic constraint Semi-definite programming Mixed-integer quadratic program Value-at-risk/variance portfolio selection |
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