Value-at-Risk (VaR) is an integral part of contemporary financial regulations. Therefore, the measurement of VaR and the design of VaR optimal portfolios are highly relevant problems for financial institutions. This paper treats a VaR constrained Markowitz style portfolio selection problem when the distribution of returns of the considered assets are given in the form of … Read more
A new algorithm for the computation of a piecewise linear function separating two finite point sets in $n$-dimensional space is developed and the algorithm is applied to solve supervised data classification problems. The algorithm computes hyperplanes incrementally and it finds as many hyperplanes as necessary to separate two sets with respect to some tolerance. An … Read more
This paper describes a problem of interdicting/jamming wireless communication networks in uncertain environments. Jamming communication networks is an important problem with many applications, but has received relatively little attention in the literature. Most of the work on network interdiction is focused on preventing jamming and analyzing network vulnerabilities. Here, we consider the case where there … Read more
In this paper formulation and solution technique using Genetic algorithms (GAs) for Optimizing the flexural capacity of steel fiber reinforced concrete beams, with random orientated steel fibers, is presented along with identification of design variables, objective function and constraints. The most important factors which influence the ultimate load carrying capacity of FRC are the volume … Read more
A standard quadratic optimization problem (StQP) consists in minimizing a quadratic form over a simplex. A number of problems can be transformed into a StQP, including the general quadratic problem over a polytope and the maximum clique problem in a graph. In this paper we present several polynomial-time bounds for StQP ranging from very simple … Read more
The Hartree-Fock method is well known in quantum chemistry, and widely used to obtain atomic and molecular eletronic wave functions, based on the minimization of a functional of the energy. This gives rise to a multi-extremal, nonconvex, polynomial optimization problem. We give a novel mathematical programming formulation of the problem, which we solve by using … Read more
We establish new lower bounds on the distance between two points of a minimum energy configuration of $N$ points in $\mathbb{R}^3$ interacting according to a pairwise potential function. For the Lennard-Jones case, this bound is 0.67985 (and 0.7633 in the planar case). A similar argument yields an estimate for the minimal distance in Morse clusters, … Read more
The evolutionary history of species may be described by a phylogenetic tree whose topology captures ancestral relationships among the species, and whose branch lengths denote evolution times. For a fixed topology and an assumed probabilistic model of nucleotide substitution, we show that the likelihood of a given tree is a d.c. (difference of convex) function … Read more
We describe scheduling algorithms for monitoring an information source whose contents change at times modeled by a nonhomogeneous Poisson process. In a given time period of length T, we enforce a politeness constraint that we may only probe the source at most n times. This constraint, along with an optional constraint that no two probes … Read more
The problem of finding the optimal placement of $N$ identical, non overlapping, circles with maximum radius in the unit square is a well known challenge both in classical geometry and in optimization. A database of putative optima is currently maintained at \url{www.packomania.com}. Recently, through clever use of an extremely simple global optimization method, we succeeded … Read more