We present experimental results on portfolio optimization problems with return errors under the robust optimization framework. We use several a histogram-like model for return deviations, and a model that allows correlation among errors, together with a cutting-plane algorithm which proves effective for large, real-life data sets. CitationColumbia Center for Financial Engineering Report 2007-01 Columbia University, … Read more
We provide explicit sufficient conditions for a polynomial $f$ to be a sum of squares (s.o.s.), linear in the coefficients of $f$. All conditions are simple and provide an explicit description of a convex polyhedral subcone of the cone of s.o.s. polynomials of degree at most $2d$. We also provide a simple condition to ensure … Read more
We investigate and discuss when the inverse of a multivariate truncated moment matrix of a measure has zeros in some prescribed entries. We describe precisely which pattern of these zeroes corresponds to independence, namely, the measure having a product structure. A more refined finding is that the key factor forcing a zero entry in this … Read more
Given $z\in C^n$ and $A\in Z^{m\times n}$, we consider the problem of evaluating the counting function $h(y;z):=\sum\{z^x : x \in Z^n; Ax = y, x \geq 0\}$. We provide an explicit expression for $h(y;z)$ as well as an algorithm with possibly numerous but simple computations. In addition, we exhibit finitely many fixed convex cones of … Read more
This paper focuses on a multi-objective derivation of branch-and-bound procedures. Such a procedure aims to provide the set of Pareto optimal solutions of a multi-objective combinatorial optimization problem. Unlike previous works on this issue, the bounding is performed here via a set of points rather than a single ideal point. The main idea is that … Read more
Variational data assimilation is used at major weather prediction centers to produce the initial conditions for 7- to 10-day weather forecasts. This technique requires the solution of a very large data-fitting problem in which the major element is a set of partial differential equations that models the evolution of the atmosphere over a time window … Read more
In this paper, we study extensions of the classical Markowitz mean-variance portfolio optimization model. First, we consider that the expected asset returns are stochastic by introducing a probabilistic constraint which imposes that the expected return of the constructed portfolio must exceed a prescribed return threshold with a high confidence level. We study the deterministic equivalents … Read more
Let C be the convex hull of points {(1;x)(1,x’)| x \in F\subset R^n}. Representing or approximating C is a fundamental problem for global optimization algorithms based on convex relaxations of products of variables. If n
In adversarial environments, disabling the communication capabilities of the enemy is a high priority. We introduce the problem of determining the optimal number and locations for a set of jamming devices in order to neutralize a wireless communication network. This problem is known as the WIRELESS NETWORK JAMMING PROBLEM. We develop several mathematical programming formulations … Read more
In this paper we address the following probabilistic version (PSC) of the set covering problem: $min \{ cx \ |\ {\mathbb P} (Ax\ge \xi) \ge p,\ x_{j}\in \{0,1\}^N\}$ where $A$ is a 0-1 matrix, $\xi$ is a random 0-1 vector and $p\in (0,1]$ is the threshold probability level. We formulate (PSC) as a mixed integer … Read more