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We study the combination of proximal gradient descent with multigrid for solving a class of possibly nonsmooth strongly convex optimization problems. We propose a multigrid proximal gradient method called MGProx, which accelerates the…

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.…

We introduce a generic scheme to solve nonconvex optimization problems using gradient-based algorithms originally designed for minimizing convex functions. Even though these methods may originally require convexity to operate, the proposed…

We study the problem of minimizing a $m$-weakly convex and possibly nonsmooth function. Weak convexity provides a broad framework that subsumes convex, smooth, and many composite nonconvex functions. In this work, we propose a…

Gradient compression is of growing interests for solving constrained optimization problems including compressed sensing, noisy recovery and matrix completion under limited communication resources and storage costs. Convergence analysis of…

This paper considers a class of convex optimization problems where both, the objective function and the constraints, have a continuously varying dependence on time. Our goal is to develop an algorithm to track the optimal solution as it…

We consider simple bilevel optimization problems where the goal is to compute among the optimal solutions of a composite convex optimization problem, one that minimizes a secondary objective function. Our main contribution is threefold. (i)…

This paper investigates a subgradient-based algorithm to solve the system identification problem for linear time-invariant systems with non-smooth objectives. This is essential for robust system identification in safety-critical…

We propose several adaptive algorithmic methods for problems of non-smooth convex optimization. The first of them is based on a special artificial inexactness. Namely, the concept of inexact ($ \delta, \Delta, L$)-model of objective…

In this paper we consider convergence rate problems for stochastic strongly-convex optimization in the non-Euclidean sense with a constraint set over a time-varying multi-agent network. We propose two efficient non-Euclidean stochastic…

In this paper, we consider a class of constrained multiobjective optimization problems, where each objective function can be expressed by adding a possibly nonsmooth nonconvex function and a differentiable function with Lipschitz continuous…

We consider the problem of maximizing a convex function over a closed convex set in a real Hilbert space. For linear functions, we show that a single orthogonal projection suffices to obtain an approximate solution. For continuous convex…

We consider stochastic convex optimization problems, where several machines act asynchronously in parallel while sharing a common memory. We propose a robust training method for the constrained setting and derive non asymptotic convergence…

Despite the broad use of fixed-point iterations throughout applied mathematics, the optimal convergence rate of general fixed-point problems with nonexpansive nonlinear operators has not been established. This work presents an acceleration…

Constrained non-convex optimization is fundamentally challenging, as global solutions are generally intractable and constraint qualifications may not hold. However, in many applications, including safe policy optimization in control and…

A very popular approach for solving stochastic optimization problems is the stochastic gradient descent method (SGD). Although the SGD iteration is computationally cheap and the practical performance of this method may be satisfactory under…

In this paper, we address the distributed optimization problem over unidirectional networks with possibly time-invariant heterogeneous bounded transmission delays. In particular, we propose a modified version of the Accelerated Distributed…

We analyze the convergence of gradient-based optimization algorithms that base their updates on delayed stochastic gradient information. The main application of our results is to the development of gradient-based distributed optimization…

In this paper we study convex bi-level optimization problems for which the inner level consists of minimization of the sum of smooth and nonsmooth functions. The outer level aims at minimizing a smooth and strongly convex function over the…

This paper develops a unified distributed method for solving two classes of constrained networked optimization problems, i.e., optimal consensus problem and resource allocation problem with non-identical set constraints. We first transform…