We present a coordinate ascent method for a class of semidefinite programming problems that arise in non-convex quadratic integer optimization. These semidefinite programs are characterized by a small total number of active constraints and by low-rank constraint matrices. We exploit this special structure by solving the dual problem, using a barrier method in combination with … Read more
The purpose of this paper is to solve the 0-1 k-item quadratic knapsack problem (kQKP), a problem of maximizing a quadratic function subject to two linear constraints.We propose an exact method based on semide nite optimization. The semide nite relaxation used in our approach includes simple rank one constraints, which can be handled efficiently by interior point … Read more
We introduce the Asynchronous PALM algorithm, a new extension of the Proximal Alternating Linearized Minimization (PALM) algorithm for solving nonconvex nonsmooth optimization problems. Like the PALM algorithm, each step of the Asynchronous PALM algorithm updates a single block of coordinates; but unlike the PALM algorithm, the Asynchronous PALM algorithm eliminates the need for sequential updates … Read more
Optimization-based bound tightening (OBBT) is one of the most effective procedures to reduce variable domains of nonconvex mixed-integer nonlinear programs (MINLPs). At the same time it is one of the most expensive bound tightening procedures, since it solves auxiliary linear programs (LPs)—up to twice the number of variables many. The main goal of this paper … Read more
This paper focuses on coordinate update methods, which are useful for solving problems involving large or high-dimensional datasets. They decompose a problem into simple subproblems, where each updates one, or a small block of, variables while fixing others. These methods can deal with linear and nonlinear mappings, smooth and nonsmooth functions, as well as convex … Read more
We study the polyhedral structure of the static probabilistic lot-sizing (SPLS) problem and propose facets that subsume existing inequalities for this problem. In addition, the proposed inequalities give the convex hull description of a related stochastic lot-sizing problem. We propose a new compact formulation that exploits the simple recourse structure, which can be applied to … Read more
We develop a modular and tractable framework for solving an adaptive distributionally robust linear opti- mization problem, where we minimize the worst-case expected cost over an ambiguity set of probability dis- tributions. The adaptive distrbutaionally robust optimization framework caters for dynamic decision making, where decisions can adapt to the uncertain outcomes as they unfold in … Read more
Traditional stochastic programs assume that the probability distribution of uncertainty is known. However, in practice, the probability distribution oftentimes is not known or cannot be accurately approximated. One way to address such distributional ambiguity is to work with distributionally robust convex stochastic programs (DRSPs), which minimize the worst-case expected cost with respect to a set … Read more
This paper investigates the use of phi-divergences in ambiguous (or distributionally robust) two-stage stochastic programs. Classical stochastic programming assumes the distribution of uncertain parameters are known. However, the true distribution is unknown in many applications. Especially in cases where there is little data or not much trust in the data, an ambiguity set of distributions … Read more
In this paper we propose an inexact proximal point method to solve equilibrium problem using proximal distances and the diagonal subdi erential. Under some natural assumptions on the problem and the quasimonotonicity condition on the bifunction, we prove that the sequence generated for the method converges to a solution point of the problem. CitationReport01-2016-PESC-COPPE-UFRJArticleDownload View PDF