Related papers: Nonlinear preconditioned primal-dual method for a …

We propose a primal-dual smoothing framework for finding a near-stationary point of a class of non-smooth non-convex optimization problems with max-structure. We analyze the primal and dual gradient complexities of the framework via two…

We develop an inexact primal-dual first-order smoothing framework to solve a class of non-bilinear saddle point problems with primal strong convexity. Compared with existing methods, our framework yields a significant improvement over the…

Using convex combination and linesearch techniques, we introduce a novel primal-dual algorithm for solving structured convex-concave saddle point problems with a generic smooth nonbilinear coupling term. Our adaptive linesearch strategy…

In this paper, we investigate a class of constrained saddle point (SP) problems where the objective function is nonconvex-concave and smooth. This class of problems has wide applicability in machine learning, including robust multi-class…

This paper studies the primal-dual convergence and iteration-complexity of proximal bundle methods for solving nonsmooth problems with convex structures. More specifically, we develop a family of primal-dual proximal bundle methods for…

We provide an overview of primal-dual algorithms for nonsmooth and non-convex-concave saddle-point problems. This flows around a new analysis of such methods, using Bregman divergences to formulate simplified conditions for convergence.

We study preconditioned proximal point methods for a class of saddle point problems, where the preconditioner decouples the overall proximal point method into an alternating primal--dual method. This is akin to the Chambolle--Pock method or…

Based on the needs of convergence proofs of preconditioned proximal point methods, we introduce notions of partial strong submonotonicity and partial (metric) subregularity of set-valued maps. We study relationships between these two…

We propose an extended primal-dual algorithm framework for solving a general nonconvex optimization model. This work is motivated by image reconstruction problems in a class of nonlinear imaging, where the forward operator can be formulated…

In this paper, we propose a descent method for composite optimization problems with linear operators. Specifically, we first design a structure-exploiting preconditioner tailored to the linear operator so that the resulting preconditioned…

We consider the problem of minimizing a convex, separable, nonsmooth function subject to linear constraints. The numerical method we propose is a block-coordinate extension of the Chambolle-Pock primal-dual algorithm. We prove convergence…

This paper addresses constrained smooth saddle-point problems in settings where projection onto the feasible sets is computationally expensive. We bridge the gap between projection-based and projection-free optimization by introducing a…

We consider a generic convex-concave saddle point problem with separable structure, a form that covers a wide-ranged machine learning applications. Under this problem structure, we follow the framework of primal-dual updates for saddle…

We present a primal-dual algorithmic framework to obtain approximate solutions to a prototypical constrained convex optimization problem, and rigorously characterize how common structural assumptions affect the numerical efficiency. Our…

In this paper, we propose a new primal-dual algorithmic framework for a class of convex-concave saddle point problems frequently arising from image processing and machine learning. Our algorithmic framework updates the primal variable…

In this paper, we propose a new decomposition approach named the proximal primal dual algorithm (Prox-PDA) for smooth nonconvex linearly constrained optimization problems. The proposed approach is primal-dual based, where the primal step…

A new primal-dual algorithm is presented for solving a class of non-convex minimization problems. This algorithm is based on canonical duality theory such that the original non-convex minimization problem is first reformulated as a…

We consider convex-concave saddle point problems with a separable structure and non-strongly convex functions. We propose an efficient stochastic block coordinate descent method using adaptive primal-dual updates, which enables flexible…

In this paper we propose a primal-dual dynamical approach to the minimization of a structured convex function consisting of a smooth term, a nonsmooth term, and the composition of another nonsmooth term with a linear continuous operator. In…

Employing the ideas of non-linear preconditioning and testing of the classical proximal point method, we formalise common arguments in convergence rate and convergence proofs of optimisation methods to the verification of a simple…