Related papers: Generalized Reduced Jacobian Method

We extend the Malitsky-Tam forward-reflected-backward (FRB) splitting method for inclusion problems of monotone operators to nonconvex minimization problems. By assuming the generalized concave Kurdyka-{\L}ojasiewicz (KL) property of a…

We derive an explicit formula, as well as an efficient procedure, for constructing a generalized Jacobian for the projector of a given square matrix onto the Birkhoff polytope, i.e., the set of doubly stochastic matrices. To guarantee the…

We consider the sequence acceleration problem for the alternating direction method-of-multipliers (ADMM) applied to a class of equality-constrained problems with strongly convex quadratic objectives, which frequently arise as the Newton…

A novel three-term Polak-Ribi\`{e}re-Polyak conjugate gradient method is proposed for solving vector optimization problems. It should be emphasized that this is the first extension of three-term conjugate gradient methods from scalar…

Policy optimization, which finds the desired policy by maximizing value functions via optimization techniques, lies at the heart of reinforcement learning (RL). In addition to value maximization, other practical considerations arise as…

This work focuses on convergence analysis of the projected gradient method for solving constrained convex minimization problem in Hilbert spaces. We show that the sequence of points generated by the method employing the Armijo linesearch…

A simple alternative to the conjugate gradient(CG) method is presented; this method is developed as a special case of the more general iterated Ritz method (IRM) for solving a system of linear equations. This novel algorithm is not based on…

Based on differences of points and differences of gradients over the most recent three iterations, together with the Taylor's theorem, two forms of the quasi-Newton equations at the recent iteration are constructed. By using the two forms…

The Scheduled Relaxation Jacobi (SRJ) method is a viable candidate as a high performance linear solver for elliptic partial differential equations (PDEs). The method greatly improves the convergence of the standard Jacobi iteration by…

Solving symmetric positive semidefinite linear systems is an essential task in many scientific computing problems. While Jacobi-type methods, including the classical Jacobi method and the weighted Jacobi method, exhibit simplicity in their…

With the advancement of neural networks, diverse methods for neural Granger causality have emerged, which demonstrate proficiency in handling complex data, and nonlinear relationships. However, the existing framework of neural Granger…

We consider the convergence of iterative solvers for problems of nonlinear magnetostatics. Using the equivalence to an underlying minimization problem, we can establish global linear convergence of a large class of methods, including the…

We consider the problem of finding sparse solutions to a system of underdetermined nonlinear system of equations. The methods are based on a Gauss-Newton approach with line search where the search direction is found by solving a linearized…

Accompanied with the rising popularity of compressed sensing, the Alternating Direction Method of Multipliers (ADMM) has become the most widely used solver for linearly constrained convex problems with separable objectives. In this work, we…

We consider optimization problems in which the goal is find a $k$-dimensional subspace of $\mathbb{R}^n$, $k<<n$, which minimizes a convex and smooth loss. Such problems generalize the fundamental task of principal component analysis (PCA)…

We study projection-free methods for constrained Riemannian optimization. In particular, we propose the Riemannian Frank-Wolfe (RFW) method. We analyze non-asymptotic convergence rates of RFW to an optimum for (geodesically) convex…

In this paper, we develop a new Randomized Global Generalized Minimum Residual (RGlGMRES) algorithm for efficiently computing solutions to large scale linear systems with multiple right hand sides.The proposed method builds on a recently…

We present an efficient algorithm for least-squares constrained nuclear norm minimization, a computationally challenging problem with broad applications. Our approach combines a level set method with secant iterations and a proximal…

Markov decision processes (MDPs) with large number of states are of high practical interest. However, conventional algorithms to solve MDP are computationally infeasible in this scenario. Approximate dynamic programming (ADP) methods tackle…

Existing results for low-rank matrix recovery largely focus on quadratic loss, which enjoys favorable properties such as restricted strong convexity/smoothness (RSC/RSM) and well conditioning over all low rank matrices. However, many…