For a set of financial securities specified by their expected returns and variance/covariances we propose the concept of minimum risk arbitrage, characterize conditions under which such opportunities may exist. We use conic duality and convex analysis to derive these characterizations. For practical computation a decidability result on the existence of an arbitrage opportunity is derived. … Read more
A GRASP (greedy randomized adaptive search procedure) is a multi-start metaheuristic for combinatorial optimization. We study the probability distributions of solution time to a sub-optimal target value in five GRASPs that have appeared in the literature and for which source code is available. The distributions are estimated by running 12,000 independent runs of the heuristic. … Read more
In this paper we introduce a generalization of stable sets: stable multi-sets. A stable multi-set is an assignment of integers to the vertices of a graph, such that specified bounds on vertices and edges are not exceeded. In case all vertex and edge bounds equal one, stable multi-sets are equivalent to stable sets. For the … Read more
We consider the multi-stage multiprocessor flowshop scheduling problem with uniform machines at each stage and the minimum makespan objective. Using a vector summation technique, three polynomial-time heuristics are developed with absolute worst-case performance guarantees. As a direct corollary, in the special case of the ordinary flowshop problem we come to the best approximation algorithms (both … Read more
Networks 39 (2002), 216-231. CitationNetworks 39 (2002), 216-231.
A slack-based feasible interior point method is described which can be derived as a modification of infeasible methods. The modification is minor for most line search methods, but trust region methods require special attention. It is shown how the Cauchy point, which is often computed in trust region methods, must be modified so that the … Read more
In this paper we study two strengthened semidefinite programming relaxations for the Max-Cut problem. Our results hold for every instance of Max-Cut; in particular, we make no assumptions about the edge weights. We prove that the first relaxation provides a strengthening of the Goemans-Williamson relaxation. The second relaxation is a further tightening of the first … Read more
This paper demonstrates that for generalized methods of multipliers for convex programming based on Bregman distance kernels — including the classical quadratic method of multipliers — the minimization of the augmented Lagrangian can be truncated using a simple, generally implementable stopping criterion based only on the norms of the primal iterate and the gradient (or … Read more
In this paper we present a new bound on the min-cut max-flow ratio for multicommodity flow problems. We use a so-called aggregated commodity formulation and an optimal solution to its dual to show our main result. Currently, the best known bound for this ratio is proportional to log(k) where k is the number of origin-destination … Read more
We investigate the solution of large scale instances of the capacitated and uncapacitated facility location problems. Let n be the number of customers and m the number of potential facility sites. For the uncapacitated case we solved instances of size m x n=3000 x 3000; for the capacitated case the largest instances were 1000 x … Read more