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Algorithm for cardinality-constrained quadratic optimization

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Abstract

This paper describes an algorithm for cardinality-constrained quadratic optimization problems, which are convex quadratic programming problems with a limit on the number of non-zeros in the optimal solution. In particular, we consider problems of subset selection in regression and portfolio selection in asset management and propose branch-and-bound based algorithms that take advantage of the special structure of these problems. We compare our tailored methods against CPLEX’s quadratic mixed-integer solver and conclude that the proposed algorithms have practical advantages for the special class of problems we consider.

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Authors and Affiliations

  1. Sloan School of Management and Operations Research Center, Massachusetts Institute of Technology, E53-363, Cambridge, MA, 02139, USA

    Dimitris Bertsimas

  2. Department of Combinatorics and Optimization, Faculty of Mathematics, University of Waterloo, Waterloo, ON, N2L 3G1, Canada

    Romy Shioda

Authors
  1. Dimitris Bertsimas
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  2. Romy Shioda
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Correspondence to Romy Shioda.

Additional information

The research of D. Bertsimas was partially supported by the Singapore-MIT alliance.

The research of R. Shioda was partially supported by the Singapore-MIT alliance, the Discovery Grant from NSERC and a research grant from the Faculty of Mathematics, University of Waterloo.

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Bertsimas, D., Shioda, R. Algorithm for cardinality-constrained quadratic optimization. Comput Optim Appl 43, 1–22 (2009). https://doi.org/10.1007/s10589-007-9126-9

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  • DOI: https://doi.org/10.1007/s10589-007-9126-9

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