Related papers: Proximal Diagonal Newton Methods for Composite Opt…
We present a proximal gradient method for solving convex multiobjective optimization problems, where each objective function is the sum of two convex functions, with one assumed to be continuously differentiable. The algorithm incorporates…
Recently, the proximal Newton-type method and its variants have been generalized to solve composite optimization problems over the Stiefel manifold whose objective function is the summation of a smooth function and a nonsmooth function. In…
In this paper, we consider the composite optimization problems over the Stiefel manifold. A successful method to solve this class of problems is the proximal gradient method proposed by Chen et al. Motivated by the proximal Newton-type…
The motivation for this paper stems from the desire to develop an adaptive sampling method for solving constrained optimization problems in which the objective function is stochastic and the constraints are deterministic. The method…
We present a novel Newton-type method for distributed optimization, which is particularly well suited for stochastic optimization and learning problems. For quadratic objectives, the method enjoys a linear rate of convergence which provably…
In this work, we generalized and unified recent two completely different works of Jascha \cite{sohl2014fast} and Lee \cite{lee2012proximal} respectively into one by proposing the \textbf{prox}imal s\textbf{to}chastic \textbf{N}ewton-type…
In this paper, we propose a new Fully Composite Formulation of convex optimization problems. It includes, as a particular case, the problems with functional constraints, max-type minimization problems, and problems of Composite…
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…
We propose several new nonsmooth Newton methods for solving convex composite optimization problems with polyhedral regularizers, while avoiding the computation of complicated second-order information on these functions. Under the…
Decentralized optimization is well studied for smooth unconstrained problems. However, constrained problems or problems with composite terms are an open direction for research. We study structured (or composite) optimization problems, where…
Composite optimization problems, where the sum of a smooth and a merely lower semicontinuous function has to be minimized, are often tackled numerically by means of proximal gradient methods as soon as the lower semicontinuous part of the…
In this paper, we propose two algorithms for solving convex optimization problems with linear ascending constraints. When the objective function is separable, we propose a dual method which terminates in a finite number of iterations. In…
Newton's method is a fundamental technique in optimization with quadratic convergence within a neighborhood around the optimum. However reaching this neighborhood is often slow and dominates the computational costs. We exploit two…
We present two approximate versions of the proximal subgradient method for minimizing the sum of two convex functions (not necessarily differentiable). The algorithms involve, at each iteration, inexact evaluations of the proximal operator…
A Newton-type active set algorithm for large-scale minimization subject to polyhedral constraints is proposed. The algorithm consists of a gradient projection step, a second-order Newton-type step in the null space of the constraint matrix,…
This paper describes a method for solving smooth nonconvex minimization problems subject to bound constraints with good worst-case complexity guarantees and practical performance. The method contains elements of two existing methods: the…
This work proposes an implementable proximal-type method for a broad class of optimization problems involving nonsmooth and nonconvex objective and constraint functions. In contrast to existing methods that rely on an ad hoc model…
The proximal gradient descent method, well-known for composite optimization, can be completely described by the concept of proximal gradient mapping. In this paper, we highlight our previous two discoveries of proximal gradient…
In this paper we propose a variant of the random coordinate descent method for solving linearly constrained convex optimization problems with composite objective functions. If the smooth part of the objective function has Lipschitz…
We consider minimizing a function consisting of a quadratic term and a proximable term which is possibly nonconvex and nonsmooth. This problem is also known as scaled proximal operator. Despite its simple form, existing methods suffer from…