We focus in this paper the problem of improving the semidefinite programming (SDP) relaxations for the standard quadratic optimization problem (standard QP in short) that concerns with minimizing a quadratic form over a simplex. We first analyze the duality gap between the standard QP and one of...

In this paper we investigate a class of cardinality-constrained portfolio selection problems. We construct convex relaxations for this class of optimization problems via a new Lagrangian decomposition scheme. We show that the dual problem can be reduced to a second-order cone program problem...

The rank function rank(.) is neither continuous nor convex which brings much difficulty to the solution of rank minimization problems. In this paper, we provide a unified framework to construct the approximation functions of rank(.), and study their favorable properties. Particularly, with two...

In this paper we consider optimal control problems subject to a semilinear elliptic state equation together with the control constraints 0≤u≤1 and ∫u=m. Optimality conditions for this problem are derived and reformulated as a nonlinear, nonsmooth equation which is solved using a semismooth...

In this paper, we introduce a new method, called the Lattice Projection Method (LPM), for solving eigenvalue complementarity problems. The original problem is reformulated to find the roots of a nonsmooth function. A semismooth Newton type method is then applied to approximate the eigenvalues...