Related papers: Matrix-free stochastic calculation of operator nor…
This paper develops a new class of algorithms for general linear systems and eigenvalue problems. These algorithms apply fast randomized sketching to accelerate subspace projection methods, such as GMRES and Rayleigh--Ritz. This approach…
In this paper, a gradient-free distributed algorithm is introduced to solve a set constrained optimization problem under a directed communication network. Specifically, at each time-step, the agents locally compute a so-called…
We present new algorithms for the randomized construction of hierarchically semi-separable matrices, addressing several practical issues. The HSS construction algorithms use a partially matrix-free, adaptive randomized projection scheme to…
In this paper, we propose a sampling algorithm based on state-of-the-art statistical machine learning techniques to obtain conditional nonlinear optimal perturbations (CNOPs), which is different from traditional (deterministic) optimization…
This work proposes block-coordinate fixed point algorithms with applications to nonlinear analysis and optimization in Hilbert spaces. The asymptotic analysis relies on a notion of stochastic quasi-Fej\'er monotonicity, which is thoroughly…
We consider the problem of uniform sampling of points on an algebraic variety. Specifically, we develop a randomized algorithm that, given a small set of multivariate polynomials over a sufficiently large finite field, produces a common…
An operator analogue of the FEAST matrix eigensolver is developed to compute the discrete part of the spectrum of a differential operator in a region of interest in the complex plane. Unbounded search regions are handled with a novel…
In this paper, we study a Markov chain-based stochastic gradient algorithm in general Hilbert spaces, aiming at approximating the optimal solution of a quadratic loss function. We establish probabilistic upper bounds on its convergence. We…
We study reward-free reinforcement learning (RL) with linear function approximation, where the agent works in two phases: (1) in the exploration phase, the agent interacts with the environment but cannot access the reward; and (2) in the…
This paper proposes an arc-search interior-point algorithm for the nonlinear constrained optimization problem. The proposed algorithm uses the second-order derivatives to construct a search arc that approaches the optimizer. Because the arc…
This document introduces a strategy to solve linear optimization problems. The strategy is based on the bounding condition each constraint produces on each one of the problem's dimension. The solution of a linear optimization problem is…
This article presents a randomized matrix-free method for approximating the trace of $f({\bf A})$, where ${\bf A}$ is a large symmetric matrix and $f$ is a function analytic in a closed interval containing the eigenvalues of ${\bf A}$. Our…
We propose in this paper a unifying scheme for several algorithms from the literature dedicated to the solving of monotone inclusion problems involving compositions with linear continuous operators in infinite dimensional Hilbert spaces. We…
Two optimization algorithms are proposed for solving a stochastic programming problem for which the objective function is given in the form of the expectation of convex functions and the constraint set is defined by the intersection of…
In this work we study symmetric random matrices with variance profile satisfying certain conditions. We establish the convergence of the operator norm of these matrices to the largest element of the support of the limiting empirical…
This paper studies the matrix completion problem under arbitrary sampling schemes. We propose a new estimator incorporating both max-norm and nuclear-norm regularization, based on which we can conduct efficient low-rank matrix recovery…
We investigate the techniques and ideas used in the convergence analysis of two proximal ADMM algorithms for solving convex optimization problems involving compositions with linear operators. Besides this, we formulate a variant of the ADMM…
In this article, we propose a splitting algorithm to find zeros of the sum of four maximally monotone operators in real Hilbert spaces. In particular, we consider a Lipschitzian operator, a cocoercive operator, and a linear composite term.…
We propose an inertial forward-backward splitting algorithm to compute the zero of a sum of two monotone operators allowing for stochastic errors in the computation of the operators. More precisely, we establish almost sure convergence in…
This Note is inspired by the recent paper by Djafary Rouhani and Moradi [J. Optim. Theory Appl. 172 (2017) 222-235], where a proximal point algorithm proposed by Boikanyo and Moro\c{s}anu [Optim. Lett. 7 (2013) 415-420] is discussed. We…