Related papers: A variable metric forward--backward method with ex…
This work is concerned with the classical problem of finding a zero of a sum of maximal monotone operators. For the projective splitting framework recently proposed by Combettes and Eckstein, we show how to replace the fundamental…
Conventional inverse optimization inputs a solution and finds the parameters of an optimization model that render a given solution optimal. The literature mostly focuses on inferring the objective function in linear problems when accepted…
We propose a novel continuous-time algorithm for inequality-constrained convex optimization inspired by proportional-integral control. Unlike the popular primal-dual gradient dynamics, our method includes a proportional term to control the…
In this paper we develop a stochastic heavy ball method for solving ill-posed inverse problems. The method updates the iterate using only a randomly selected equation at each iteration step while incorporating a momentum term into the…
In this paper we propose a new fast splitting algorithm to solve the Weighted Split Bregman minimization problem in the backward step of an accelerated Forward-Backward algorithm. Beside proving the convergence of the method, numerical…
In this paper, we propose a framework based on sum-of-squares programming to design iterative first-order optimization algorithms for smooth and strongly convex problems. Our starting point is to develop a polynomial matrix inequality as a…
This work presents an approach to the inverse design of scattering systems by modifying the transmission matrix using reinforcement learning. We utilize Proximal Policy Optimization to navigate the highly non-convex landscape of the object…
The article is devoted to the development of algorithmic methods ensuring efficient complexity bounds for strongly convex-concave saddle point problems in the case when one of the groups of variables is high-dimensional, and the other is…
This paper presents and investigates an inexact proximal gradient method for solving composite convex optimization problems characterized by an objective function composed of a sum of a full-domain differentiable convex function and a…
In this article we propose a method for solving unconstrained optimization problems with convex and Lipschitz continuous objective functions. By making use of the Moreau envelopes of the functions occurring in the objective, we smooth the…
In this paper, we approach the problem of finding the zeros of the sum of a maximally monotone operator and a monotone and Lipschitz continuous one in a real Hilbert space via an implicit forward-backward-forward dynamical system with…
Extrapolation is a well-known technique for solving convex optimization and variational inequalities and recently attracts some attention for non-convex optimization. Several recent works have empirically shown its success in some machine…
We develop a computationally efficient algorithm for the automatic regularization of nonlinear inverse problems based on the discrepancy principle. We formulate the problem as an equality constrained optimization problem, where the…
In this paper, we propose a variable metric version of Tseng's algorithm (the forward-backward-forward algorithm: FBF) combined with extrapolation from the past that includes error terms for finding a zero of the sum of a maximally monotone…
Self-supervised representation learning has seen remarkable progress in the last few years, with some of the recent methods being able to learn useful image representations without labels. These methods are trained using backpropagation,…
Modern technology often generates data with complex structures in which both response and explanatory variables are matrix-valued. Existing methods in the literature are able to tackle matrix-valued predictors but are rather limited for…
Two characteristics that make convex decomposition algorithms attractive are simplicity of operations and generation of parallelizable structures. In principle, these schemes require that all coordinates update at the same time, i.e., they…
Composite minimization involves a collection of smooth functions which are aggregated in a nonsmooth manner. In the convex setting, we design an algorithm by linearizing each smooth component in accordance with its main curvature. The…
This paper presents new approaches for finding the determinant and inverse of a matrix. The choice of pivot selection is kept arbitrary and can be made according to the users need. So the ill conditioned matrices can be handled easily. The…
The nonlinear, or warped, resolvent recently explored by Giselsson and B\`ui-Combettes has been used to model a large set of existing and new monotone inclusion algorithms. To establish convergent algorithms based on these resolvents,…