Related papers: Inexact proximal methods for weakly convex functio…

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…

We consider a nonsmooth optimization problem on Riemannian manifold, whose objective function is the sum of a differentiable component and a nonsmooth convex function. We propose a manifold inexact augmented Lagrangian method (MIALM) for…

This paper concerns a class of constrained optimization problems in which, the objective and constraint functions are both upper-$\mathcal{C}^2$. For such nonconvex and nonsmooth optimization problems, we develop an inexact moving balls…

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…

We study a class of nonconvex-nonconcave minimax problems in which the inner maximization problem satisfies a local Kurdyka-Lojasiewicz (KL) condition that may vary with the outer minimization variable. In contrast to the global KL or…

We study the convergence issue for inexact descent algorithm (employing general step sizes) for multiobjective optimizations on general Riemannian manifolds (without curvature constraints). Under the assumption of the local…

This paper deals with convex nonsmooth optimization problems. We introduce a general smooth approximation framework for the original function and apply random (accelerated) coordinate descent methods for minimizing the corresponding smooth…

In this paper we consider stochastic weakly convex composite problems, however without the existence of a stochastic subgradient oracle. We present a derivative free algorithm that uses a two point approximation for computing a gradient…

This paper presents two inexact composite gradient methods, one inner accelerated and another doubly accelerated, for solving a class of nonconvex spectral composite optimization problems. More specifically, the objective function for these…

We introduce a class of stochastic algorithms for minimizing weakly convex functions over proximally smooth sets. As their main building blocks, the algorithms use simplified models of the objective function and the constraint set, along…

Proximal gradient methods are a popular tool for the solution of structured, nonsmooth minimization problems. In this work, we investigate an extension of the former to general Banach spaces and provide worst-case convergence rates for,…

This paper considers the robust phase retrieval problem, which can be cast as a nonsmooth and nonconvex optimization problem. We propose a new inexact proximal linear algorithm with the subproblem being solved inexactly. Our contributions…

We consider minimization of stochastic functionals that are compositions of a (potentially) non-smooth convex function $h$ and smooth function $c$ and, more generally, stochastic weakly-convex functionals. We develop a family of stochastic…

In this paper we introduce a novel abstract descent scheme suited for the minimization of proper and lower semicontinuous functions. The proposed abstract scheme generalizes a set of properties that are crucial for the convergence of…

We propose new proximal bundle algorithms for minimizing a nonsmooth convex function. These algorithms are derived from the application of Nesterov fast gradient methods for smooth convex minimization to the so-called Moreau-Yosida…

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…

We consider the problem of minimizing the sum of a smooth function $h$ with a bounded Hessian, and a nonsmooth function. We assume that the latter function is a composition of a proper closed function $P$ and a surjective linear map $\cal…

In this paper we propose two proximal gradient algorithms for fractional programming problems in real Hilbert spaces, where the numerator is a proper, convex and lower semicontinuous function and the denominator is a smooth function, either…

This paper extends the algorithm schemes proposed in \cite{Nesterov2007a} and \cite{Nesterov2007b} to the minimization of the sum of a composite objective function and a convex function. Two proximal point-type schemes are provided and…

We study the worst-case convergence rates of the proximal gradient method for minimizing the sum of a smooth strongly convex function and a non-smooth convex function whose proximal operator is available. We establish the exact worst-case…