This article aims to explain the Nested Benders algorithm for the solution of large-scale stochastic programming problems in a way that is intelligible to someone coming to it for the first time. In doing so it gives an explanation of Benders decomposition and of its application to two-stage stochastic programming problems (also known in this … Read more
We present two decomposition algorithms for single product deep-sea maritime inventory routing problems (MIRPs) that possess a core substructure common in many real-world applications. The problem involves routing vessels, each belonging to a particular vessel class, between loading and discharging ports, each belonging to a particular region. Our algorithms iteratively solve a MIRP by zooming … Read more
In this paper we study decomposition methods based on separable approximations for minimizing the augmented Lagrangian. In particular, we study and compare the Diagonal Quadratic Approximation Method (DQAM) of Mulvey and Ruszczy\'{n}ski and the Parallel Coordinate Descent Method (PCDM) of Richt\'{a}rik and Tak\'{a}\v{c}. We show that the two methods are equivalent for feasibility problems up … Read more
We consider a class of decomposition methods for variational inequalities, which is related to the classical Dantzig–Wolfe decomposition of linear programs. Our approach is rather general, in that it can be used with set-valued or nonmonotone operators, as well as various kinds of approximations in the subproblems of the functions and derivatives in the single-valued … Read more
In this work we consider the symmetric network equilibrium problem formulated as convex minimization problem whose variables are the path flows. In order to take into account the difficulties related to the large dimension of real network problems we adopt a column generation strategy and we employ a gradient projection method within an inexact decomposition … Read more
We present a new approach for exactly solving chance-constrained mathematical programs having discrete distributions with nite support and random polyhedral constraints. Such problems have been notoriously difficult to solve due to nonconvexity of the feasible region, and most available methods are only able to nd provably good solutions in certain very special cases. Our approach … Read more
The principle underlying this paper is the basic observation that the problem of simultaneously solving a large class of composite monotone inclusions and their duals can be reduced to that of finding a zero of the sum of a maximally monotone operator and a linear skew-adjoint operator. An algorithmic framework is developed for solving this … Read more
One of the main concerns of national statistical agencies (NSAs) is to publish tabular data. NSAs have to guarantee that no private information from specific respondents can be disclosed from the released tables. The purpose of the statistical disclosure control field is to avoid such a leak of private information. Most protection techniques for tabular … Read more
Although stochastic programming is a powerful tool for modeling decision-making under uncertainty, various impediments have historically prevented its wide-spread use. One key factor involves the ability of non-specialists to easily express stochastic programming problems as extensions of deterministic models, which are often formulated first. A second key factor relates to the difficulty of solving stochastic … Read more
For a risk-averse multistage stochastic optimization problem with a finite scenario tree, we introduce a new scenario decomposition method and we prove its convergence. The method is applied to a risk-averse inventory and assembly problem. In addition, we develop a partially regularized bundle method for nonsmooth optimization. Citation RUTCOR, Rutgers University, Piscataway, NJ 08854 Article … Read more