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We propose a proximal variable smoothing algorithm for nonsmooth optimization problem with sum of three functions involving weakly convex composite function. The proposed algorithm is designed as a time-varying forward-backward splitting…
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…
Backtracking line-search is an old yet powerful strategy for finding a better step sizes to be used in proximal gradient algorithms. The main principle is to locally find a simple convex upper bound of the objective function, which in turn…
Recent progress in robust statistical learning has mainly tackled convex problems, like mean estimation or linear regression, with non-convex challenges receiving less attention. Phase retrieval exemplifies such a non-convex problem,…
In this paper we propose an adaptively extrapolated proximal gradient method, which is based on the accelerated proximal gradient method (also known as FISTA), however we locally optimize the extrapolation parameter by carrying out an exact…
This paper proposes a novel CTA (Combine-Then-Adapt)-based decentralized algorithm for solving convex composite optimization problems over undirected and connected networks. The local loss function in these problems contains both smooth and…
We prove novel convergence results for a stochastic proximal gradient algorithm suitable for solving a large class of convex optimization problems, where a convex objective function is given by the sum of a smooth and a possibly non-smooth…
We introduce and analyze an algorithm for the minimization of convex functions that are the sum of differentiable terms and proximable terms composed with linear operators. The method builds upon the recently developed smoothed gap…
An adaptive regularization algorithm for unconstrained nonconvex optimization is proposed that is capable of handling inexact objective-function and derivative values, and also of providing approximate minimizer of arbitrary order. In…
We propose a new relative-error inexact version of the alternating direction method of multipliers (ADMM) for convex optimization. We prove the asymptotic convergence of our main algorithm as well as pointwise and ergodic…
For quasi-linear interface problems with discontinuous diffusion coefficients, the nonconvex objective functional often leads to optimization stagnation in randomized neural network approximations. This paper Proposes a…
We consider the problem of minimizing a convex objective which is the sum of a smooth part, with Lipschitz continuous gradient, and a nonsmooth part. Inspired by various applications, we focus on the case when the nonsmooth part is a…
The Inexact Restoration approach has proved to be an adequate tool for handling the problem of minimizing an expensive function within an arbitrary feasible set by using different degrees of precision in the objective function. The Inexact…
We develop model-based methods for solving stochastic convex optimization problems, introducing the approximate-proximal point, or aProx, family, which includes stochastic subgradient, proximal point, and bundle methods. When the modeling…
Hierarchical optimization refers to problems with interdependent decision variables and objectives, such as minimax and bilevel formulations. While various algorithms have been proposed, existing methods and analyses lack adaptivity in…
Adaptive regularized framework using cubics has emerged as an alternative to line-search and trust-region algorithms for smooth nonconvex optimization, with an optimal complexity amongst second-order methods. In this paper, we propose and…
In this paper, we propose an inertial accelerated primal-dual method for the linear equality constrained convex optimization problem. When the objective function has a ``nonsmooth + smooth'' composite structure, we further propose an…
This paper considers an online proximal-gradient method to track the minimizers of a composite convex function that may continuously evolve over time. The online proximal-gradient method is inexact, in the sense that: (i) it relies on an…
Nonconvex optimization problems arise in different research fields and arouse lots of attention in signal processing, statistics and machine learning. In this work, we explore the accelerated proximal gradient method and some of its…
In this paper, we present a novel nonlinear programming-based approach to fine-tune pre-trained neural networks to improve robustness against adversarial attacks while maintaining high accuracy on clean data. Our method introduces…