Sparse solutions of linear complementarity problems

This paper considers the characterization and computation of sparse solutions and least-p-norm solutions of the linear complementarity problem . We show that the number of non-zero entries of any least-p-norm solution of the is less than or equal to the rank of M for any arbitrary matrix M and any number , and there is such that all least-p-norm solutions for are sparse solutions. Moreover, we provide conditions on M such that a sparse solution can be found by solving convex minimization. Applications to the problem of portfolio selection within the Markowitz mean-variance framework are discussed.