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Our work considers the optimization of the sum of a non-smooth convex function and a finite family of composite convex functions, each one of which is composed of a convex function and a bounded linear operator. This type of problem is…
The recently developed Distributed Block Proximal Method, for solving stochastic big-data convex optimization problems, is studied in this paper under the assumption of constant stepsizes and strongly convex (possibly non-smooth) local…
An efficient proximal-gradient-based method, called proximal extrapolated gradient method, is designed for solving monotone variational inequality in Hilbert space. The proposed method extends the acceptable range of parameters to obtain…
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 analyze the local convergence of proximal splitting algorithms to solve optimization problems that are convex besides a rank constraint. For this, we show conditions under which the proximal operator of a function involving the rank…
We present a distributed proximal-gradient method for optimizing the average of convex functions, each of which is the private local objective of an agent in a network with time-varying topology. The local objectives have distinct…
One of the most important problems in the field of distributed optimization is the problem of minimizing a sum of local convex objective functions over a networked system. Most of the existing work in this area focus on developing…
It is well known that there have been many numerical algorithms for solving nonsmooth minimax problems, numerical algorithms for nonsmooth minimax problems with joint linear constraints are very rare. This paper aims to discuss optimality…
Denoiser models have become powerful tools for inverse problems, enabling the use of pretrained networks to approximate the score of a smoothed prior distribution. These models are often used in heuristic iterative schemes aimed at solving…
An outlier-resistance phase retrieval algorithm based on alternating direction method of multipliers (ADMM) is devised in this letter. Instead of the widely used least squares criterion that is only optimal for Gaussian noise environment,…
In this paper we propose a linear scalarization proximal point algorithm for solving arbitrary lower semicontinuous quasiconvex multiobjective minimization problems. Under some natural assumptions and using the condition that the proximal…
Non-smooth regularization is widely used in image reconstruction to eliminate the noise while preserving subtle image structures. In this work, we investigate the use of proximal Newton (PN) method to solve an optimization problem with a…
Block-coordinate algorithms are recognized to furnish efficient iterative schemes for addressing large-scale problems, especially when the computation of full derivatives entails substantial memory requirements and computational efforts. In…
This paper studies efficient distributed optimization methods for multi-agent networks. Specifically, we consider a convex optimization problem with a globally coupled linear equality constraint and local polyhedra constraints, and develop…
In this paper we analyze a class of nonconvex optimization problem from the viewpoint of abstract convexity. Using the respective generalizations of the subgradient we propose an abstract notion proximal operator and derive a number of…
In this paper, we consider a class of structured nonsmooth fractional minimization, where the first part of the objective is the ratio of a nonnegative nonsmooth nonconvex function to a nonnegative nonsmooth convex function, while the…
This paper develops the proximal method of multipliers for a class of nonsmooth convex optimization. The method generates a sequence of minimization problems (subproblems). We show that the sequence of approximations to the solutions of the…
This paper considers the robust phase retrieval, which can be cast as a nonsmooth and nonconvex composite optimization problem. We propose two first-order algorithms with adaptive step sizes: the subgradient algorithm (AdaSubGrad) and the…
Asynchronous parallel optimization algorithms for solving large-scale machine learning problems have drawn significant attention from academia to industry recently. This paper proposes a novel algorithm, decoupled asynchronous proximal…
We address composite optimization problems, which consist in minimizing the sum of a smooth and a merely lower semicontinuous function, without any convexity assumptions. Numerical solutions of these problems can be obtained by proximal…