Near-optimal solutions to large scale facility location problems

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

Solving Steiner tree problems in graphs with Lagrangian relaxation

This paper presents an algorithm to obtain near optimal solutions for the Steiner tree problem in graphs. It is based on a Lagrangian relaxation of a multi-commodity flow formulation of the problem. An extension of the subgradient algorithm, the volume algorithm, has been used to obtain lowe r bounds and to estimate primal solutions. Due … Read more

A BFGS-IP algorithm for solving strongly convex optimization problems with feasibility enforced by an exact penalty approach

This paper introduces and analyses a new algorithm for minimizing a convex function subject to a finite number of convex inequality constraints. It is assumed that the Lagrangian of the problem is strongly convex. The algorithm combines interior point methods for dealing with the inequality constraints and quasi-Newton techniques for accelerating the convergence. Feasibility of … Read more

WASP: a Wavelet Adaptive Solver for boundary value Problems – Short Reference Manual

This is a short guide to use the Matlab package WASP designed for the numerical solution of two-point linear boundary value problems that arise typically in linear quadratic optimal control. The method relies upon an adaptive computation of discretization based on a wavelet analysis. On a given refined grid, finite differences of various order are … Read more