Related papers: On the convergence analysis of one-shot inversion …
We present a novel deep learning approach to approximate the solution of large, sparse, symmetric, positive-definite linear systems of equations. These systems arise from many problems in applied science, e.g., in numerical methods for…
In this paper, we consider the nonsmooth convex optimization problems over the fixed point constraint sets of firmly nonexpansive operators. To find an optimal solution of the problem, we present an iterative method based on the hybrid…
We study a general class of bilevel problems, consisting in the minimization of an upper-level objective which depends on the solution to a parametric fixed-point equation. Important instances arising in machine learning include…
This paper is devoted to first-order algorithms for smooth convex optimization with inexact gradients. Unlike the majority of the literature on this topic, we consider the setting of relative rather than absolute inexactness. More…
The single-step one-shot method has proven to be very efficient for PDE-constrained optimization where the partial differential equation (PDE) is solved by an iterative fixed point solver. In this approach, the simulation and optimization…
In this paper, we propose a unified convergence analysis for a class of generic shuffling-type gradient methods for solving finite-sum optimization problems. Our analysis works with any sampling without replacement strategy and covers many…
We consider the problem of reconstructing an infinite set of sparse, finite-dimensional vectors, that share a common sparsity pattern, from incomplete measurements. This is in contrast to the work [17], where the single vector signal can be…
In this work, we present a method to perform 2D and 3D omnidirectional pressure integration from velocity measurements with a single-iteration matrix inversion approach. This work builds upon our previous work, where the rotating parallel…
A stochastic-gradient-based interior-point algorithm for minimizing a continuously differentiable objective function (that may be nonconvex) subject to bound constraints is presented, analyzed, and demonstrated through experimental results.…
A wide range of applications arising in machine learning and signal processing can be cast as convex optimization problems. These problems are often ill-posed, i.e., the optimal solution lacks a desired property such as uniqueness or…
The recently introduced Gradient Methods with Memory use a subset of the past oracle information to create an accurate model of the objective function that enables them to surpass the Gradient Method in practical performance. The model…
In this paper, we propose a proximal gradient method and an accelerated proximal gradient method for solving composite optimization problems, where the objective function is the sum of a smooth and a convex, possibly nonsmooth, function. We…
In this paper, we introduce a new iterative method which we call one step back approach: the main idea is to anticipate the consequence of the iterative computation per coordinate and to optimize on the choice of the sequence of the…
This paper investigates the asymmetric low-rank matrix completion problem, which can be formulated as an unconstrained non-convex optimization problem with a nonlinear least-squares objective function, and is solved via gradient descent…
Interpreting gradient methods as fixed-point iterations, we provide a detailed analysis of those methods for minimizing convex objective functions. Due to their conceptual and algorithmic simplicity, gradient methods are widely used in…
We consider centralized and distributed mirror descent algorithms over a finite-dimensional Hilbert space, and prove that the problem variables converge to an optimizer of a possibly nonsmooth function when the step sizes are square…
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…
We study the use of novel techniques arising in machine learning for inverse problems. Our approach replaces the complex forward model by a neural network, which is trained simultaneously in a one-shot sense when estimating the unknown…
For strongly convex objectives that are smooth, the classical theory of gradient descent ensures linear convergence relative to the number of gradient evaluations. An analogous nonsmooth theory is challenging. Even when the objective is…
Efficient computation of min-max problems is a central question in optimization, learning, games, and controls. Arguably the most natural algorithm is gradient-descent-ascent (GDA). However, since the 1970s, conventional wisdom has argued…