Accelerated and Inexact forward-backward algorithms

We propose a convergence analysis of accelerated forward-backward splitting methods for minimizing composite functions, when the proximity operator is not available in closed form, and is thus computed up to a certain precision. We prove that the $1/k^2$ convergence rate for the function values can be achieved if the admissible errors are of a certain … Read more

Sell or Hold: a simple two-stage stochastic combinatorial optimization problem

There are $n$ individual assets and $k$ of them are to be sold over two stages. The first-stage prices are known and the second-stage prices have a known distribution. The sell or hold problem (SHP) is to determine which assets are to be sold at each stage to maximize the total expected revenue. We show … Read more

Proximal point method on Finslerian manifolds and the “Effort Accuracy Trade off”

In this paper we consider minimization problems with constraints. We will show that if the set of constraints is a Finslerian manifold of non positive flag curvature, and the objective function is di fferentiable and satisfi es the property Kurdyka-Lojasiewicz, then the proximal point method is naturally extended to solve that class of problems. We will prove … Read more

Inexact and accelerated proximal point algorithms

We present inexact accelerated proximal point algorithms for minimizing a proper lower semicon- tinuous and convex function. We carry on a convergence analysis under different types of errors in the evaluation of the proximity operator, and we provide corresponding convergence rates for the objective function values. The proof relies on a generalization of the strategy … Read more

An efficient semidefinite programming relaxation for the graph partition problem

We derive a new semidefinite programming relaxation for the general graph partition problem (GPP). Our relaxation is based on matrix lifting with matrix variable having order equal to the number of vertices of the graph. We show that this relaxation is equivalent to the Frieze-Jerrum relaxation [A. Frieze and M. Jerrum. Improved approximation algorithms for … Read more

Decision Making under Uncertainty when Preference Information is Incomplete

We consider the problem of optimal decision making under uncertainty but assume that the decision maker’s utility function is not completely known. Instead, we consider all the utilities that meet some criteria, such as preferring certain lotteries over certain other lotteries and being risk averse, s-shaped, or prudent. This extends the notion of stochastic dominance. … Read more

A Python/C library for bound-constrained global optimization with continuous GRASP

This paper describes libcgrpp, a GNU-style dynamic shared Python/C library of the continuous greedy randomized adaptive search procedure (C-GRASP) for bound constrained global optimization. C-GRASP is an extension of the GRASP metaheuristic (Feo and Resende, 1989). After a brief introduction to C-GRASP, we show how to download, install, configure, and use the library through an … Read more

A conjugate directions approach to improve the limited-memory BFGS method

Simple modifiations of the limited-memory BFGS method (L-BFGS) for large scale unconstrained optimization are considered, which consist in corrections (derived from the idea of conjugate directions) of the used difference vectors, utilizing information from the preceding iteration. In case of quadratic objective functions, the improvement of convergence is the best one in some sense and … Read more

Simulation Optimization for the Stochastic Economic Lot Scheduling Problem

We study simulation optimization methods for the stochastic economic lot scheduling problem. In contrast to prior research, we focus on methods that treat this problem as a black box. Based on a large-scale numerical study, we compare approximate dynamic programming with a global search for parameters of simple control policies. We propose two value function … Read more

An Alternating Direction Method for Total Variation Denoising

We consider the image denoising problem using total variation (TV) regularization. This problem can be computationally challenging to solve due to the non-differentiability and non-linearity of the regularization term. We propose an alternating direction augmented Lagrangian (ADAL) method, based on a new variable splitting approach that results in subproblems that can be solved efficiently and … Read more