Related papers: Operator Splitting Performance Estimation: Tight c…

We study the applicability of the Peaceman-Rachford (PR) splitting method for solving nonconvex optimization problems. When applied to minimizing the sum of a strongly convex Lipschitz differentiable function and a proper closed function,…

We use semidefinite programming to bound the fractional cut-cover parameter of graphs in association schemes in terms of their smallest eigenvalue. We also extend the equality cases of a primal-dual inequality involving the…

In the following paper we present a new type of optimization algorithms adapted for neural network training. These algorithms are based upon sequential operator splitting technique for some associated dynamical systems. Furthermore, we…

Building on the blueprint from Goemans and Williamson (1995) for the Max-Cut problem, we construct a polynomial-time approximation algorithm for orthogonally constrained quadratic optimization problems. First, we derive a semidefinite…

Nonlinear elliptic problems arise in many fields, including plasma physics, astrophysics, and optimal transport. In this article, we propose a novel operator-splitting/finite element method for solving such problems. We begin by introducing…

In this work, we aim to establish the exact worst-case convergence rates of Douglas--Rachford splitting (DRS) and Davis--Yin splitting (DYS) when applied to convex optimization problems. Both DRS and DYS have two variants as swapping the…

There exist several methods of calculating a similarity curve, or a sequence of similarity values, representing the lexical cohesion of successive text constituents, e.g., paragraphs. Methods for deciding the locations of fragment…

We propose and analyze a second-order Strang splitting method for a class of stiff matrix differential equations with Sylvester-type structure. The method splits the dynamics into a stiff linear part, treated exactly via matrix…

Dynamic program slicing can significantly reduce the code developers need to inspect by narrowing it down to only a subset of relevant program statements. However, despite an extensive body of research showing its usefulness, dynamic…

In this paper, we prove that the ergodic sequence generated by the Peaceman-Rachford (PR) splitting method with semi-proximal terms converges for convex optimization problems (COPs). Numerical experiments on the linear programming benchmark…

Continuing earlier investigations, we analyze the convergence of operator splitting procedures combined with spatial discretization and rational approximations.

Minimizing sum of two functions under a linear constraint is what we called splitting problem. This convex optimization has wide applications in machine learning problems, such as Lasso, Group Lasso and Sparse logistic regression. A recent…

We propose a splitting approach to solve the second-order Hamilton--Jacobi equation, reducing it to a heat step and a purely first-order step. The latter is implemented using a gradient value policy iteration algorithm, enabling efficient…

The linear complementarity problem (LCP) is a general set membership problem that includes quadratic cone programming as a special case. In this work we consider a homogeneous embedding of the LCP, which encodes both the optimality…

This paper is about how to partition decision variables while decomposing a large-scale optimization problem for the best performance of distributed solution methods. Solving a large-scale optimization problem sequen- tially can be…

We consider a popular family of constrained optimization problems arising in machine learning that involve optimizing a non-decomposable evaluation metric with a certain thresholded form, while constraining another metric of interest.…

We provide a novel computer-assisted technique for systematically analyzing first-order methods for optimization. In contrast with previous works, the approach is particularly suited for handling sublinear convergence rates and stochastic…

The goal of this paper is to study approaches to bridge the gap between first-order and second-order type methods for composite convex programs. Our key observations are: i) Many well-known operator splitting methods, such as…

The three operator splitting scheme was recently proposed by [Davis and Yin, 2015] as a method to optimize composite objective functions with one convex smooth term and two convex (possibly non-smooth) terms for which we have access to…

Along with developing of Peaceman-Rachford Splittling Method (PRSM), many batch algorithms based on it have been studied very deeply. But almost no algorithm focused on the performance of stochastic version of PRSM. In this paper, we…