A difference of convex formulation of value-at-risk constrained optimization

In this article, we present a representation of value-at-risk (VaR) as a difference of convex (D.C.) functions in the case where the distribution of the underlying random variable is discrete and has finitely many atoms. The D.C. representation is used to study a financial risk-return portfolio selection problem with a VaR constraint. A branch-and-bound algorithm … Read more

D.C. Versus Copositive Bounds for Standard QP

The standard quadratic program (QPS) is $\min_{x\in\Delta} x’Qx$, where $\Delta\subset\Re^n$ is the simplex $\Delta=\{ x\ge 0 : \sum_{i=1}^n x_i=1 \}$. QPS can be used to formulate combinatorial problems such as the maximum stable set problem, and also arises in global optimization algorithms for general quadratic programming when the search space is partitioned using simplices. One … Read more