相关论文: A smoothing Anderson acceleration algorithm for no…

Partially observable Markov decision processes (POMDPs) is a rich mathematical framework that embraces a large class of complex sequential decision-making problems under uncertainty with limited observations. However, the complexity of…

The problem of minimizing the sum of nonsmooth, convex objective functions defined on a real Hilbert space over the intersection of fixed point sets of nonexpansive mappings, onto which the projections cannot be efficiently computed, is…

This work aims to solve a stochastic nonconvex nonsmooth composite optimization problem. Previous works on composite optimization problem requires the major part to satisfy Lipschitz smoothness or some relaxed smoothness conditions, which…

This paper deals with convex nonsmooth optimization problems. We introduce a general smooth approximation framework for the original function and apply random (accelerated) coordinate descent methods for minimizing the corresponding smooth…

Multilinear systems play an important role in scientific calculations of practical problems. In this paper, we consider a tensor splitting method with a relaxed Anderson acceleration for solving multilinear systems. The new method preserves…

In this paper, we focus on finding the global minimizer of a general unconstrained nonsmooth nonconvex optimization problem. Taking advantage of the smoothing method and the consensus-based optimization (CBO) method, we propose a novel…

This paper proposes and develops new Newton-type methods to solve structured nonconvex and nonsmooth optimization problems with justifying their fast local and global convergence by means of advanced tools of variational analysis and…

In this paper, we introduce the notion of generalized $\epsilon$-stationarity for a class of nonconvex and nonsmooth composite minimization problems on compact Riemannian submanifold embedded in Euclidean space. To find a generalized…

Riemannian accelerated gradient methods have been well studied for smooth optimization, typically treating geodesically convex and geodesically strongly convex cases separately. However, their extension to nonsmooth problems on manifolds…

Non-smooth optimization models play a fundamental role in various disciplines, including engineering, science, management, and finance. However, classical algorithms for solving such models often struggle with convergence speed,…

We give a complete characterization of the behavior of the Anderson acceleration (with arbitrary nonzero mixing parameters) on linear problems. Let n be the grade of the residual at the starting point with respect to the matrix defining the…

We exploit analogies between first-order algorithms for constrained optimization and non-smooth dynamical systems to design a new class of accelerated first-order algorithms for constrained optimization. Unlike Frank-Wolfe or projected…

We propose a general formulation of nonconvex and nonsmooth sparse optimization problems with convex set constraint, which can take into account most existing types of nonconvex sparsity-inducing terms, bringing strong applicability to a…

Although Anderson acceleration (AA) is known to speed up fixed-point iterations, it is rarely applied in constrained optimization, in particular sequential quadratic programming (SQP). We show that the local convergence behavior of a…

Non-smooth optimization is a core ingredient of many imaging or machine learning pipelines. Non-smoothness encodes structural constraints on the solutions, such as sparsity, group sparsity, low-rank and sharp edges. It is also the basis for…

In this work, we extend a modified Anderson acceleration proposed in [Y. He, arXiv:2603.25983, 2026] to accelerate the Picard iteration for the Navier-Stokes equations. In this variant of Anderson acceleration, named AAg, the nonlinear…

Stochastic composition optimization draws much attention recently and has been successful in many emerging applications of machine learning, statistical analysis, and reinforcement learning. In this paper, we focus on the composition…

Motivated by variational models in continuum mechanics, we introduce a novel algorithm to perform nonsmooth and nonconvex minimizations with linear constraints in Euclidean spaces. We show how this algorithm is actually a natural…

The Uzawa algorithm is an iterative method for the solution of saddle-point problems, which arise in many applications, including fluid dynamics. Viewing the Uzawa algorithm as a fixed- point iteration, we explore the use of Anderson…

In this paper, we propose a general class of algorithms for optimizing an extensive variety of nonsmoothly penalized objective functions that satisfy certain regularity conditions. The proposed framework utilizes the…