Related papers: Parallel Graver Basis Extraction for Nonlinear Int…

We propose a practical inexact augmented Lagrangian method (iALM) for nonconvex problems with nonlinear constraints. We characterize the total computational complexity of our method subject to a verifiable geometric condition, which is…

Inexact alternating direction multiplier methods (ADMMs) are developed for solving general separable convex optimization problems with a linear constraint and with an objective that is the sum of smooth and nonsmooth terms. The approach…

In this paper we investigate the parallelization of two modular algorithms. In fact, we consider the modular computation of Gr\"obner bases (resp. standard bases) and the modular computation of the associated primes of a zero-dimensional…

First-order methods for solving convex optimization problems have been at the forefront of mathematical optimization in the last 20 years. The rapid development of this important class of algorithms is motivated by the success stories…

We propose an exact algorithm for solving the longest simple path problem between two given vertices in undirected weighted graphs. By using graph partitioning and dynamic programming, we obtain an algorithm that is significantly faster…

This paper investigates a category of constrained fractional optimization problems that emerge in various practical applications. The objective function for this category is characterized by the ratio of a numerator and denominator, both…

In this paper, we accomplish a unified convergence analysis of a second-order method of multipliers (i.e., a second-order augmented Lagrangian method) for solving the conventional nonlinear conic optimization problems.Specifically, the…

In view of the existing limitations of sequential computing, parallelization has emerged as an alternative in order to improve the speedup of numerical simulations. In the framework of evolutionary problems, space-time parallel methods…

We propose HAMSI (Hessian Approximated Multiple Subsets Iteration), which is a provably convergent, second order incremental algorithm for solving large-scale partially separable optimization problems. The algorithm is based on a local…

In this paper, we consider a proximal linearized alternating direction method of multipliers (PL-ADMM) for solving linearly constrained nonconvex and possibly nonsmooth optimization problems. The algorithm is generalized by using variable…

We propose a new algorithm for multiplying dense polynomials with integer coefficients in a parallel fashion, targeting multi-core processor architectures. Complexity estimates and experimental comparisons demonstrate the advantages of this…

An influential 1990 paper of Hochbaum and Shanthikumar made it common wisdom that "convex separable optimization is not much harder than linear optimization" [JACM 1990]. We exhibit two fundamental classes of mixed integer (linear) programs…

We present an approach to solving problems in micromechanics that is amenable to massively parallel calculations through the use of graphical processing units and other accelerators. The problems lead to nonlinear differential equations…

The augmented Lagrangian method (ALM) is a benchmark for convex programming problems with linear constraints; ALM and its variants for linearly equality-constrained convex minimization models have been well studied in the literature.…

In this paper, we consider the problem of stochastic optimization, where the objective function is in terms of the expectation of a (possibly non-convex) cost function that is parametrized by a random variable. While the convergence speed…

Integer and mixed-integer nonlinear programming (INLP, MINLP) are central to logistics, energy, and scheduling, but remain computationally challenging. This survey examines how machine learning and reinforcement learning can enhance exact…

There has been significant recent progress on algorithms for approximating graph spanners, i.e., algorithms which approximate the best spanner for a given input graph. Essentially all of these algorithms use the same basic LP relaxation, so…

A step-search sequential quadratic programming method is proposed for solving nonlinear equality constrained stochastic optimization problems. It is assumed that constraint function values and derivatives are available, but only stochastic…

Multi-objective integer or mixed-integer programming problems typically have disconnected feasible domains, making the task of constructing an approximation of the Pareto front challenging. The present paper shows that certain algorithms…

Our study is motivated by the solution of Mixed-Integer Non-Linear Programming (MINLP) problems with separable non-convex functions via the Sequential Convex MINLP technique, an iterative method whose main characteristic is that of solving,…