Related papers: An inexact alternating projection method with appl…
A fundamental class of matrix optimization problems that arise in many areas of science and engineering is that of quadratic optimization with orthogonality constraints. Such problems can be solved using line-search methods on the Stiefel…
The idea of a finite collection of closed sets having "strongly regular intersection" at a given point is crucial in variational analysis. We show that this central theoretical tool also has striking algorithmic consequences. Specifically,…
This paper considers the robust phase retrieval problem, which can be cast as a nonsmooth and nonconvex optimization problem. We propose a new inexact proximal linear algorithm with the subproblem being solved inexactly. Our contributions…
This work proposes an implementable proximal-type method for a broad class of optimization problems involving nonsmooth and nonconvex objective and constraint functions. In contrast to existing methods that rely on an ad hoc model…
In this paper, we focus on the problem of minimizing the sum of a nonconvex differentiable function and a DC (Difference of Convex functions) function, where the differentiable function is not restricted to the global Lipschitz gradient…
We present an algorithm for the solution of Sylvester equations with right-hand side of low rank. The method is based on projection onto a block rational Krylov subspace, with two key contributions with respect to the state-of-the-art.…
This paper provides a theoretical and numerical investigation of a penalty decomposition scheme for the solution of optimization problems with geometric constraints. In particular, we consider some situations where parts of the constraints…
This paper presents an adaptive sampling algorithm tailored for the optimization of parametrized dynamical systems using projection-based model order reduction. Unlike classical sampling strategies, this framework does not aim for a small…
This paper analyzes the iteration-complexity of a quadratic penalty accelerated inexact proximal point method for solving linearly constrained nonconvex composite programs. More specifically, the objective function is of the form $f + h$…
We consider projection algorithms for solving (nonconvex) feasibility problems in Euclidean spaces. Of special interest are the Method of Alternating Projections (MAP) and the Douglas-Rachford or Averaged Alternating Reflection Algorithm…
In this paper, we develop a novel accelerated fixed-point-based framework using delayed inexact oracles to approximate a fixed point of a nonexpansive operator (or equivalently, a root of a co-coercive operator), a central problem in…
We propose two new alternating direction methods to solve "fully" nonsmooth constrained convex problems. Our algorithms have the best known worst-case iteration-complexity guarantee under mild assumptions for both the objective residual and…
The solution of sequences of shifted linear systems is a classic problem in numerical linear algebra, and a variety of efficient methods have been proposed over the years. Nevertheless, there still exist challenging scenarios witnessing a…
We develop two adaptive discretization algorithms for convex semi-infinite optimization, which terminate after finitely many iterations at approximate solutions of arbitrary precision. In particular, they terminate at a feasible point of…
In this paper, we present a unified analysis of matrix completion under general low-dimensional structural constraints induced by {\em any} norm regularization. We consider two estimators for the general problem of structured matrix…
We consider the problem of matrix completion on an $n \times m$ matrix. We introduce the problem of Interpretable Matrix Completion that aims to provide meaningful insights for the low-rank matrix using side information. We show that the…
Variable order structures model situations in which the comparison between two points depends on a point-to-cone map. In this paper, an inexact projected gradient method for solving smooth constrained vector optimization problems on…
This work proposes a novel convex-non-convex formulation of the image segmentation and the image completion problems. The proposed approach is based on the minimization of a functional involving two distinct regularization terms: one…
In this paper we derive a Newton type method to solve the non-linear system formed by combining the Tikhonov normal equations and Morozov's discrepancy principle. We prove that by placing a bound on the step size of the Newton iterations…
Smoothing accelerated gradient methods achieve faster convergence rates than that of the subgradient method for some nonsmooth convex optimization problems. However, Nesterov's extrapolation may require gradients at infeasible points, and…