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In this paper we present a convergence rate analysis of inexact variants of several randomized iterative methods. Among the methods studied are: stochastic gradient descent, stochastic Newton, stochastic proximal point and stochastic…
Neural network constraint satisfaction is crucial for safety-critical applications such as power system optimization, robotic path planning, and autonomous driving. However, existing constraint satisfaction methods face…
This article details a general numerical framework to approximate so-lutions to linear programs related to optimal transport. The general idea is to introduce an entropic regularization of the initial linear program. This regularized…
For many applications in signal processing and machine learning, we are tasked with minimizing a large sum of convex functions subject to a large number of convex constraints. In this paper, we devise a new random projection method (RPM) to…
The regularized Barzilai-Borwein (RBB) method represents a promising gradient-based optimization algorithm. In this paper, by splitting the gradient into two parts and analyzing the dynamical system of difference equations governing the…
The generalized alternating direction method of multipliers (ADMM) of Xiao et al. [{\tt Math. Prog. Comput., 2018}] aims at the two-block linearly constrained composite convex programming problem, in which each block is in the form of…
Recent literature has advocated the use of randomized methods for accelerating the solution of various matrix problems arising throughout data science and computational science. One popular strategy for leveraging randomization is to use it…
We study the application of the Augmented Lagrangian Method to the solution of linear ill-posed problems. Previously, linear convergence rates with respect to the Bregman distance have been derived under the classical assumption of a…
In this paper, we derive a Fast Reflected Forward-Backward (Fast RFB) algorithm to solve the problem of finding a zero of the sum of a maximally monotone operator and a monotone and Lipschitz continuous operator in a real Hilbert space. Our…
We present an accelerated, or 'look-ahead' version of the Newton-Dinkelbach method, a well-known technique for solving fractional and parametric optimization problems. This acceleration halves the Bregman divergence between the current…
The Kaczmarz and Gauss-Seidel methods both solve a linear system $\bf{X}\bf{\beta} = \bf{y}$ by iteratively refining the solution estimate. Recent interest in these methods has been sparked by a proof of Strohmer and Vershynin which shows…
Randomized iterative algorithms have attracted much attention in recent years because they can approximately solve large-scale linear systems of equations without accessing the entire coefficient matrix. In this paper, we propose two novel…
RBM-MPC is a computationally efficient variant of Model Predictive Control (MPC) in which the Random Batch Method (RBM) is used to speed up the finite-horizon optimal control problems at each iteration. In this paper, stability and…
We propose a new approach to combine Restricted Boltzmann Machines (RBMs) that can be used to solve combinatorial optimization problems. This allows synthesis of larger models from smaller RBMs that have been pretrained, thus effectively…
In this paper, based on an optimization problem, a sketch-and-project method for solving the linear matrix equation AXB = C is proposed. We provide a thorough convergence analysis for the new method and derive a lower bound on the…
In this paper, we propose a new framework for solving state estimation problems with an additional sparsity-promoting $L_1$-regularizer term. We first formulate such problems as minimization of the sum of linear or nonlinear quadratic error…
Regularized regression problems are ubiquitous in statistical modeling, signal processing, and machine learning. Sparse regression in particular has been instrumental in scientific model discovery, including compressed sensing applications,…
In this paper, we study nonconvex constrained stochastic zeroth-order optimization problems, for which we have access to exact information of constraints and noisy function values of the objective. We propose a Bregman linearized augmented…
Randomized iterative methods, such as the randomized Kaczmarz method, have gained significant attention for solving large-scale linear systems due to their simplicity and efficiency. Meanwhile, Krylov subspace methods have emerged as a…
Spectral Clustering as a relaxation of the normalized/ratio cut has become one of the standard graph-based clustering methods. Existing methods for the computation of multiple clusters, corresponding to a balanced $k$-cut of the graph, are…