Related papers: Stochastic inertial primal-dual algorithms

Conventional online multi-task learning algorithms suffer from two critical limitations: 1) Heavy communication caused by delivering high velocity of sequential data to a central machine; 2) Expensive runtime complexity for building task…

We introduce an efficient first-order primal-dual method for the solution of nonsmooth PDE-constrained optimization problems. We achieve this efficiency through not solving the PDE or its linearisation on each iteration of the optimization…

We discuss non-Euclidean deterministic and stochastic algorithms for optimization problems with strongly and uniformly convex objectives. We provide accuracy bounds for the performance of these algorithms and design methods which are…

We develop a first-order accelerated algorithm for a class of constrained bilinear saddle-point problems with applications to network systems. The algorithm is a modified time-varying primal-dual version of an accelerated mirror-descent…

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…

This paper focuses on stochastic optimal control problems with constraints in law, which are rewritten as optimization (minimization) of probability measures problem on the canonical space. We introduce a penalized version of this type of…

Stochastic compositional optimization (SCO) has attracted considerable attention because of its broad applicability to important real-world problems. However, existing works on SCO assume that the projection within a solution update is…

Pre-conditioning is a well-known concept that can significantly improve the convergence of optimization algorithms. For noise-free problems, where good pre-conditioners are not known a priori, iterative linear algebra methods offer one way…

The Primal-Dual (PD) algorithm is widely used in convex optimization to determine saddle points. While the stability of the PD algorithm can be easily guaranteed, strict contraction is nontrivial to establish in most cases. This work…

The importance of an adequate inner loop starting point (as opposed to a sufficient inner loop stopping rule) is discussed in the context of a numerical optimization algorithm consisting of nested primal-dual proximal-gradient iterations.…

We study a stochastic primal-dual method for constrained optimization over Riemannian manifolds with bounded sectional curvature. We prove non-asymptotic convergence to the optimal objective value. More precisely, for the class of…

Second-order dynamical systems are important tools for solving optimization problems, and most of existing works in this field have focused on unconstrained optimization problems. In this paper, we propose an inertial primal-dual dynamical…

We propose and analyze the convergence of a novel stochastic forward-backward splitting algorithm for solving monotone inclusions given by the sum of a maximal monotone operator and a single-valued maximal monotone cocoercive operator. This…

In this paper, we propose a unified primal-dual algorithm framework based on the augmented Lagrangian function for composite convex problems with conic inequality constraints. The new framework is highly versatile. First, it not only covers…

We propose a new first-order primal-dual optimization framework for a convex optimization template with broad applications. Our optimization algorithms feature optimal convergence guarantees under a variety of common structure assumptions…

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.

In this paper, we study inclusion problems where the involved operators may not be monotone in the classical sense. Specifically, we assume the operators to be generalized monotone, a weaker notion than classical monotonicity. This allows…

Motivated by recent results on the dual formulation of optimal stopping problems, we investigate in this short paper how the knowledge of an approximating dual martingale can improve the efficiency of primal methods. In particular, we show…

We propose in this paper a unifying scheme for several algorithms from the literature dedicated to the solving of monotone inclusion problems involving compositions with linear continuous operators in infinite dimensional Hilbert spaces. We…

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…