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Most algorithms for solving optimization problems or finding saddle points of convex-concave functions are fixed-point algorithms. In this work we consider the generic problem of finding a fixed point of an average of operators, or an…

This paper considers decentralized consensus optimization problems where nodes of a network have access to different summands of a global objective function. Nodes cooperate to minimize the global objective by exchanging information with…

We propose an iterative method for nonlinear semidefinite programs with box constraints. The search direction in the proposed method utilizes the distance from the current point to the boundary of a feasible set. The computation of the…

This paper develops and implements a practical simulation-based method for estimating dynamic discrete choice models. The method, which can accommodate lagged dependent variables, serially correlated errors, unobserved variables, and many…

The convergence analysis of a third-order scheme for the highly nonlinear Landau-Lifshitz-Gilbert equation with a non-convex constraint is considered. In this paper, we first present a fully discrete semi-implicit method for solving the…

Stochastic coordinate descent algorithms are efficient methods in which each iterate is obtained by fixing most coordinates at their values from the current iteration, and approximately minimizing the objective with respect to the remaining…

This paper considers the decision-dependent optimization problem, where the data distributions react in response to decisions affecting both the objective function and linear constraints. We propose a new method termed repeated projected…

Real life signals are in general non--stationary and non--linear. The development of methods able to extract their hidden features in a fast and reliable way is of high importance in many research fields. In this work we tackle the problem…

Path finding algorithm addresses problem of finding shortest path from source to destination avoiding obstacles. There exist various search algorithms namely A*, Dijkstra's and ant colony optimization. Unlike most path finding algorithms…

Nearest neighbor search is a fundamental data structure problem with many applications in machine learning, computer vision, recommendation systems and other fields. Although the main objective of the data structure is to quickly report…

High-dimensional time series are a core ingredient of the statistical modeling toolkit, for which numerous estimation methods are known.But when observations are scarce or corrupted, the learning task becomes much harder.The question is:…

Developing large-scale distributed methods that are robust to the presence of adversarial or corrupted workers is an important part of making such methods practical for real-world problems. Here, we propose an iterative approach that is…

This paper considers the problem of distributed model fitting using the alternating directions method of multipliers (ADMM). ADMM splits the learning problem into several smaller subproblems, usually by partitioning the data samples. The…

Many iterative methods for solving optimization or feasibility problems have been invented, and often convergence of the iterates to some solution is proven. Under favourable conditions, one might have additional bounds on the distance of…

This paper introduces a discretization-accurate stopping criterion of symmetric iterative methods for solving systems of algebraic equations resulting from the finite element approximation. The stopping criterion consists of the evaluations…

The estimation of a sparse vector in the linear model is a fundamental problem in signal processing, statistics, and compressive sensing. This paper establishes a lower bound on the mean-squared error, which holds regardless of the…

This paper proposes a partially inexact alternating direction method of multipliers for computing approximate solution of a linearly constrained convex optimization problem. This method allows its first subproblem to be solved inexactly…

Identifying differential operators from data is essential for the mathematical modeling of complex physical and biological systems where massive datasets are available. These operators must be stable for accurate predictions for dynamics…

Machine learning pipelines often rely on optimization procedures to make discrete decisions (e.g., sorting, picking closest neighbors, or shortest paths). Although these discrete decisions are easily computed, they break the…

Iterative algorithms solve problems by taking steps until a solution is reached. Models in the form of Deep Thinking (DT) networks have been demonstrated to learn iterative algorithms in a way that can scale to different sized problems at…