Algorithm for cardinality-constrained quadratic optimization

Authors:
Dimitris Bertsimas;Romy Shioda
Affiliations:
Sloan School of Management and Operations Research Center, Massachusetts Institute of Technology, E53-363, Cambridge, USA 02139;Department of Combinatorics and Optimization, Faculty of Mathematics, University of Waterloo, Waterloo, Canada N2L 3G1
Venue:
Computational Optimization and Applications
Year:
2009

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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.