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A Semidefinite Programming Heuristic for Quadratic Programming Problems with Complementarity Constraints

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Abstract

The presence of complementarity constraints brings a combinatorial flavour to an optimization problem. A quadratic programming problem with complementarity constraints can be relaxed to give a semidefinite programming problem. The solution to this relaxation can be used to generate feasible solutions to the complementarity constraints. A quadratic programming problem is solved for each of these feasible solutions and the best resulting solution provides an estimate for the optimal solution to the quadratic program with complementarity constraints. Computational testing of such an approach is described for a problem arising in portfolio optimization.

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  1. Warren & Selbert, Inc., Santa Barbara, CA, 93101, USA

    Stephen Braun & John E. Mitchell

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  1. Stephen Braun
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  2. John E. Mitchell
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Correspondence to Stephen Braun.

Additional information

Research supported in part by the National Science Foundation’s VIGRE Program (Grant DMS-9983646).

Research partially supported by NSF Grant number CCR-9901822.

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Braun, S., Mitchell, J.E. A Semidefinite Programming Heuristic for Quadratic Programming Problems with Complementarity Constraints. Comput Optim Applic 31, 5–29 (2005). https://doi.org/10.1007/s10589-005-1014-6

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