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...

This paper presents the surrogate model based algorithm SO-I for solving purely integer optimization problems that have computationally expensive black-box objective functions and that may have computationally expensive constraints. The algorithm was developed for solving global optimization...