Cardinality Constraints in quadratic optimization

*To*: mathgroup at smc.vnet.net*Subject*: [mg109680] Cardinality Constraints in quadratic optimization*From*: Richard Warnung <richard.f.warnung at gmail.com>*Date*: Tue, 11 May 2010 06:29:39 -0400 (EDT)

Hello there, I am trying to solve a problem that sounds pretty basic but it is hard to solve. Economically the task is to minimize variance of a portfolio of N assets (N e.q. 200) under some linear constraints and additionally the constraint, that at most K (K e.g. 20) assets get a weight different than zero. Mathematically this is a quadratic minimization problem with some linear and a cardinality constraint. If you search the web then this is sometimes solved via (non-linear) mixed-integer programming or various heuristics (Simmulated Annealing, genetic algorithms, ..) , but I wonder if there is a (maybe commercial) mathematica package that adresses exactly this problem. Furthermore I would be thankful for hints on which interfaces to external packages can be recommended for this task. Thanks for your help and suggestions, best regards Richard