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
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
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
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
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. Citation To appear in Journal of Convex Analysis, … Read more
We provide a sharp generalization to the nonautonomous case of the well-known Ko\-ba\-yashi estimate for proximal iterates associated with maximal monotone operators. We then derive a bound for the distance between a continuous-in-time trajectory, namely the solution to the differential inclusion $\dot{x} + A(t)x\ni 0$, and the corresponding proximal iterations. We also establish continuity properties … 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
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
In this paper, we propose a semidefinite optimization (SDP) based model for the class of minimax two-stage stochastic linear optimization problems with risk aversion. The distribution of the second-stage random variables is assumed to be chosen from a set of multivariate distributions with known mean and second moment matrix. For the minimax stochastic problem with … Read more
As a traditional model in the operations research and management science domain, lot-sizing problem is embedded in many application problems such as production and inventory planning and has been consistently drawing attentions from researchers. There is significant research progress on polynomial time algorithm developments for deterministic uncapacitated lot-sizing problems based on Wagner-and-Whitin property. However, in … Read more