Related papers: Economic inexact restoration for derivative-free e…
We develop a new proximal-gradient method for minimizing the sum of a differentiable, possibly nonconvex, function plus a convex, possibly non differentiable, function. The key features of the proposed method are the definition of a…
Derivative-free optimization problems are optimization problems where derivative information is unavailable. The least Frobenius norm updating quadratic interpolation model function is one of the essential under-determined model functions…
Inverse problems are key issues in several scientific areas, including signal processing and medical imaging. Data-driven approaches for inverse problems aim for learning model and regularization parameters from observed data samples, and…
We present a new algorithm for solving optimization problems with objective functions that are the sum of a smooth function and a (potentially) nonsmooth regularization function, and nonlinear equality constraints. The algorithm may be…
We propose a penalty-based smoothing framework for convex nonsmooth functions with a supremum structure. The regularization yields a differentiable surrogate with controlled approximation error, a single-valued dual maximizer, and explicit…
Image reconstruction in Multispectral Computed Tomography (MSCT) requires solving a challenging nonlinear inverse problem, commonly tackled via iterative optimization algorithms. Existing methods necessitate computing the derivative of the…
We consider the problem of unconstrained minimization of a smooth objective function in $\R^n$ in a setting where only function evaluations are possible. While importance sampling is one of the most popular techniques used by machine…
We introduce a derivative-free global optimization algorithm that efficiently computes minima for various classes of one-dimensional functions, including non-convex, and non-smooth functions.This algorithm numerically approximates the…
In this paper, we develop an approach to recursively estimate the quadratic risk for matrix recovery problems regularized with spectral functions. Toward this end, in the spirit of the SURE theory, a key step is to compute the (weak)…
Many machine learning solutions are framed as optimization problems which rely on good hyperparameters. Algorithms for tuning these hyperparameters usually assume access to exact solutions to the underlying learning problem, which is…
For the composite multi-objective optimization problem composed of two nonsmooth terms, a smoothing method is used to overcome the nonsmoothness of the objective function, making the objective function contain at most one nonsmooth term.…
In this work, we propose derivative-free framework for bilevel optimization. We consider both the upper and lower-level problems with bound constraints on the variables, as well as general nonlinear constraints, assuming that first-order…
In this work, we study the robust phase retrieval problem where the task is to recover an unknown signal $\theta^* \in \mathbb{R}^d$ in the presence of potentially arbitrarily corrupted magnitude-only linear measurements. We propose an…
We propose general non-accelerated and accelerated tensor methods under inexact information on the derivatives of the objective, analyze their convergence rate. Further, we provide conditions for the inexactness in each derivative that is…
The Halpern iteration for solving monotone inclusion problems has gained increasing interests in recent years due to its simple form and appealing convergence properties. In this paper, we investigate the inexact variants of the scheme in…
An adaptive regularization algorithm for unconstrained nonconvex optimization is presented in which the objective function is never evaluated, but only derivatives are used. This algorithm belongs to the class of adaptive regularization…
We study inexact fixed-point proximity algorithms for solving a class of sparse regularization problems involving the $\ell_0$ norm. Specifically, the $\ell_0$ model has an objective function that is the sum of a convex fidelity term and a…
Structured optimization problems are ubiquitous in fields like data science and engineering. The goal in structured optimization is using a prescribed set of points, called atoms, to build up a solution that minimizes or maximizes a given…
A common problem in the sciences is that a signal of interest is observed only indirectly, through smooth functionals of the signal whose values are then obscured by noise. In such inverse problems, the functionals dampen or entirely…
We investigate the convergence properties of a class of iterative algorithms designed to minimize a potentially non-smooth and noisy objective function, which may be algebraically intractable and whose values may be obtained as the output…