In this paper we present an algorithmic framework for solving a class of combinatorial optimization problems on graphs with bounded pathwidth. The problems are NP-hard in general, but solvable in linear time on this type of graphs. The problems are relevant for assessing network reliability and improving the network’s performance and fault tolerance. The main … Read more
The main goal of this paper is to develop accuracy estimates for stochastic programming problems by employing robust stochastic approximation (SA) type algorithms. To this end we show that while running a Robust Mirror Descent Stochastic Approximation procedure one can compute, with a small additional effort, lower and upper statistical bounds for the optimal objective … Read more
We present a line search algorithm for large-scale constrained optimization that is robust and efficient even for problems with (nearly) rank-deficient Jacobian matrices. The method is matrix-free (i.e., it does not require explicit storage or factorizations of derivative matrices), allows for inexact step computations, and is applicable for nonconvex problems. The main components of the … Read more
In the context of simulating the frictional contact dynamics of large systems of rigid bodies, this paper reviews a novel method for solving large cone complementarity problems by means of a fixed-point iteration algorithm. The method is an extension of the Gauss-Seidel and Gauss-Jacobimethods with overrelaxation for symmetric convex linear complementarity problems. Convergent under fairly … Read more
The present work aims at comparing the performance of several quadratic programming (QP) solvers for simulating large-scale frictional rigid-body systems. Traditional time-stepping schemes for simulation of multibody systems are formulated as linear complementarity problems (LCPs) with copositive matrices. Such LCPs are generally solved by means of Lemketype algorithms and solvers such as the PATH solver … Read more
In the Generalized Quadratic Assignment Problem (GQAP), given M facilities and N locations, one must assign each facility to one location so as to satisfy the given facility space requirements, minimizing the sum of installation and facility interaction costs. In this paper, we propose a new Lagrangean relaxation and a lower bounding procedure for the … Read more
Given an approximation $\{f_n\}$ of a given objective function $f$, we provide simple and fairly general conditions under which a diagonal proximal point algorithm approximates the value $\inf f$ at a reasonable rate. We also perform some numerical tests and present a short survey on finite convergence. CitationTo appear in Journal of Convex Analysis, 16 … Read more
Quadratic assignment problems (QAPs) with a Hamming distance matrix of a hypercube or a Manhattan distance matrix of rectangular grids arise frequently from communications and facility locations and are known to be among the hardest discrete optimization problems. In this paper we consider the issue of how to obtain lower bounds for those two classes … Read more
We consider the Tikhonov-like dynamics $-\dot u(t)\in A(u(t))+\varepsilon(t)u(t)$ where $A$ is a maximal monotone operator and the parameter function $\eps(t)$ tends to 0 for $t\to\infty$ with $\int_0^\infty\eps(t)dt=\infty$. When $A$ is the subdifferential of a closed proper convex function $f$, we establish strong convergence of $u(t)$ towards the least-norm minimizer of $f$. In the general case … Read more
We study the asymptotic behavior of almost-orbits of abstract evolution systems in Banach spaces with or without a Lipschitz assumption. In particular, we establish convergence, convergence in average and almost-convergence of almost-orbits both for the weak and the strong topologies based on the behavior of the orbits. We also analyze the set of almost-stationary points. … Read more