相关论文: On the Q-linear convergence of forward-backward sp…

The forward-backward operator splitting algorithm is one of the most important methods for solving the optimization problem of the sum of two convex functions, where one is differentiable with a Lipschitz continuous gradient and the other…

In this paper we focus on the convergence analysis of the forward-backward splitting method for solving nonsmooth optimization problems in Hilbert spaces when the objective function is the sum of two convex functions. Assuming that one of…

The forward-backward splitting algorithm is a popular operator-splitting method for solving monotone inclusion of the sum of a maximal monotone operator and a cocoercive operator. In this paper, we present a new convergence analysis of a…

In this paper, we consider the Forward--Backward proximal splitting algorithm to minimize the sum of two proper convex functions, one of which having a Lipschitz continuous gradient and the other being partly smooth relative to an active…

In this paper, we study local convergence of high-order Tensor Methods for solving convex optimization problems with composite objective. We justify local superlinear convergence under the assumption of uniform convexity of the smooth…

We present in this paper two different classes of general $K$-splitting algorithms for solving finite-dimensional convex optimization problems. Under the assumption that the function being minimized has a Lipschitz continuous gradient, we…

We develop a line-search second-order algorithmic framework for minimizing finite sums. We do not make any convexity assumptions, but require the terms of the sum to be continuously differentiable and have Lipschitz-continuous gradients.…

In this paper, we provide a generalization of the forward-backward splitting algorithm for minimizing the sum of a proper convex lower semicontinuous function and a differentiable convex function whose gradient satisfies a locally…

We study the variable metric forward-backward splitting algorithm for convex minimization problems without the standard assumption of the Lipschitz continuity of the gradient. In this setting, we prove that, by requiring only mild…

This paper studies first-order algorithms for solving fully composite optimization problems over convex and compact sets. We leverage the structure of the objective by handling its differentiable and non-differentiable components…

We consider global efficiency of algorithms for minimizing a sum of a convex function and a composition of a Lipschitz convex function with a smooth map. The basic algorithm we rely on is the prox-linear method, which in each iteration…

In this paper, we consider the problem of minimizing the sum of two convex functions subject to linear linking constraints. The classical alternating direction type methods usually assume that the two convex functions have relatively easy…

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…

This paper provides a comprehensive study of the nonmonotone forward-backward splitting (FBS) method for solving a class of nonsmooth composite problems in Hilbert spaces. The objective function is the sum of a Fr\'echet differentiable (not…

In this paper, we propose an adaptive forward-backward-forward splitting algorithm for finding a zero of a pseudo-monotone operator which is split as a sum of three operators: the first is continuous single-valued, the second is…

This paper addresses a class of general nonsmooth and nonconvex composite optimization problems subject to nonlinear equality constraints. We assume that a part of the objective function and the functional constraints exhibit local…

We propose an adaptive accelerated smoothing technique for a nonsmooth convex optimization problem where the smoothing update rule is coupled with the momentum parameter. We also extend the setting to the case where the objective function…

The standard assumption for proving linear convergence of first order methods for smooth convex optimization is the strong convexity of the objective function, an assumption which does not hold for many practical applications. In this…

The forward-backward splitting method (FBS) for minimizing a nonsmooth composite function can be interpreted as a (variable-metric) gradient method over a continuously differentiable function which we call forward-backward envelope (FBE).…

This paper introduces the generalized forward-backward splitting algorithm for minimizing convex functions of the form $F + \sum_{i=1}^n G_i$, where $F$ has a Lipschitz-continuous gradient and the $G_i$'s are simple in the sense that their…