Speaker: Prof.Xiaojun Chen（The Hong Kong Polytechnic University）

Title: Sparse Solutions of Complementarity Problems

Time: Tue, Oct.8 2019,PM:15:00-16:30

Location: Room 4318, Building No.4, Wushan Campus

Abstract：

     This talk considers the characterization and computation of sparse solutions and least-p-norm (0<p<1) solutions of the linear complementarity problem LCP(q,M). We show that the number of non-zero entries of any least-p-norm solution of the LCP(q,M) is less than or equal to the rank of M for any arbitrary matrix M and any number p\in (0,1), and there is \bar{p}\in (0,1) such that all least-p-norm solutions for  p\in (0, \bar{p}) 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. Finally, we introduce a new approximation method for solving the least-p-norm (0<p<1) solutions of the nonlinear complementarity problem.