Related papers: A Class of Accelerated Fixed-Point-Based Methods w…
In this paper we analyze several inexact fast augmented Lagrangian methods for solving linearly constrained convex optimization problems. Mainly, our methods rely on the combination of excessive-gap-like smoothing technique developed in…
We introduce a generic scheme for accelerating first-order optimization methods in the sense of Nesterov, which builds upon a new analysis of the accelerated proximal point algorithm. Our approach consists of minimizing a convex objective…
This work proposes a general strategy for solving possibly nonlinear problems arising from implicit time discretizations as a sequence of explicit solutions. The resulting sequence may exhibit instabilities similar to those of the base…
A pervasive approach in scientific computing is to express the solution to a given problem as the limit of a sequence of vectors or other mathematical objects. In many situations these sequences are generated by slowly converging iterative…
This paper addresses a distributed convex optimization problem with a class of coupled constraints, which arise in a multi-agent system composed of multiple communities modeled by cliques. First, we propose a fully distributed…
In this paper, we study nonconvex constrained optimization problems with both equality and inequality constraints, covering deterministic and stochastic settings. We propose a novel first-order algorithm framework that employs a…
Multi-time-scale stochastic approximation is an iterative algorithm for finding the fixed point of a set of $N$ coupled operators given their noisy samples. It has been observed that due to the coupling between the decision variables and…
In this paper, we develop a new type of accelerated algorithms to solve some classes of maximally monotone equations as well as monotone inclusions. Instead of using Nesterov's accelerating approach, our methods rely on a so-called…
We study the convergence of an inexact version of the classical Krasnosel'skii-Mann iteration for computing fixed points of nonexpansive maps. Our main result establishes a new metric bound for the fixed-point residuals, from which we…
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…
This paper studies a class of double-loop (inner-outer) algorithms for convex composite optimization. For unconstrained problems, we develop a restarted accelerated composite gradient method that attains the optimal first-order complexity…
Gradient-type distributed optimization methods have blossomed into one of the most important tools for solving a minimization learning task over a networked agent system. However, only one gradient update per iteration is difficult to…
Accelerated algorithms have broad applications in large-scale optimization, due to their generality and fast convergence. However, their stability in the practical setting of noise-corrupted gradient oracles is not well-understood. This…
We introduce a unified framework for iterative reasoning that leverages non-Euclidean geometry via Bregman divergences, higher-order operator averaging, and adaptive feedback mechanisms. Our analysis establishes that, under mild smoothness…
In machine learning research, the proximal gradient methods are popular for solving various optimization problems with non-smooth regularization. Inexact proximal gradient methods are extremely important when exactly solving the proximal…
We consider a framework for the construction of iterative schemes for operator equations that combine low-rank approximation in tensor formats and adaptive approximation in a basis. Under fairly general assumptions, we obtain a rigorous…
The coupled simulations of dynamic interactions between the well, hydraulic fractures and reservoir have significant importance in some areas of petroleum reservoir engineering. Several approaches to the problem of coupling between the…
This paper analyzes the iteration-complexity of a quadratic penalty accelerated inexact proximal point method for solving linearly constrained nonconvex composite programs. More specifically, the objective function is of the form $f + h$…
This paper concerns the minimization of the composition of a nonsmooth convex function and a $\mathcal{C}^{1,1}$ mapping $F$ over a $\mathcal{C}^2$-smooth embedded closed submanifold $\mathcal{M}$. For this class of nonconvex and nonsmooth…
We propose a delay-agnostic asynchronous coordinate update algorithm (DEGAS) for computing operator fixed points, with applications to asynchronous optimization. DEGAS includes novel asynchronous variants of ADMM and block-coordinate…