An Asynchronous Proximal Bundle Method

We develop a fully asynchronous proximal bundle method for solving non-smooth, convex optimization problems. The algorithm can be used as a drop-in replacement for classic bundle methods, i.e., the function must be given by a first-order oracle for computing function values and subgradients. The algorithm allows for an arbitrary number of master problem processes computing … Read more

Accelerating Domain Propagation: an Efficient GPU-Parallel Algorithm over Sparse Matrices

Fast domain propagation of linear constraints has become a crucial component of today‚Äôs best algorithms and solvers for mixed integer programming and pseudo-boolean optimization to achieve peak solving performance. Irregularities in the form of dynamic algorithmic behaviour, dependency structures, and sparsity patterns in the input data make efficient implementations of domain propagation on GPUs and, … Read more

An Inexact Spingarn’s Partial Inverse Method with Applications to Operator Splitting and Composite Optimization

We propose and study the iteration-complexity of an inexact version of the Spingarn’s partial inverse method. Its complexity analysis is performed by viewing it in the framework of the hybrid proximal extragradient (HPE) method, for which pointwise and ergodic iteration-complexity has been established recently by Monteiro and Svaiter. As applications, we propose and analyze the … Read more

On Unbounded Delays in Asynchronous Parallel Fixed-Point Algorithms

The need for scalable numerical solutions has motivated the development of asynchronous parallel algorithms, where a set of nodes run in parallel with little or no synchronization, thus computing with delayed information. This paper studies the convergence of the asynchronous parallel algorithm ARock under potentially unbounded delays. ARock is a general asynchronous algorithm that has … Read more

TMAC: A Toolbox of Modern Async-Parallel, Coordinate, Splitting, and Stochastic Methods

TMAC is a toolbox written in C++11 that implements algorithms based on a set of mod- ern methods for large-scale optimization. It covers a variety of optimization problems, which can be both smooth and nonsmooth, convex and nonconvex, as well as constrained and unconstrained. The algorithms implemented in TMAC, such as the coordinate up- date … Read more

Coordinate Friendly Structures, Algorithms and Applications

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

ARock: an Algorithmic Framework for Asynchronous Parallel Coordinate Updates

We propose ARock, an asynchronous parallel algorithmic framework for finding a fixed point to a nonexpansive operator. In the framework, a set of agents (machines, processors, or cores) update a sequence of randomly selected coordinates of the unknown variable in an asynchronous parallel fashion. As special cases of ARock, novel algorithms for linear systems, convex … Read more

Steepest Edge as Applied to the Standard Simplex Method

In this paper we discuss results and advantages of using steepest edge column choice rules and their derivatives. We show empirically, when we utilize the steepest edge column choice rule for the tableau method, that the density crossover point at which the tableau method is more efficient than the revised method drops to 5%. This … Read more

The unified framework of some proximal-based decomposition methods for monotone variational inequalities with separable structure

Some existing decomposition methods for solving a class of variational inequalities (VI) with separable structures are closely related to the classical proximal point algorithm, as their decomposed sub-VIs are regularized by proximal terms. Differing in whether the generated sub-VIs are suitable for parallel computation, these proximal-based methods can be categorized into the parallel decomposition methods … Read more

Algorithm xxx: APPSPACK 4.0: Asynchronous Parallel Pattern Search for Derivative-Free Optimization

APPSPACK is software for solving unconstrained and bound constrained optimization problems. It implements an asynchronous parallel pattern search method that has been specifically designed for problems characterized by expensive function evaluations. Using APPSPACK to solve optimization problems has several advantages: No derivative information is needed; the procedure for evaluating the objective function can be executed … Read more