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Shor's r-algorithm (Shor, Zhurbenko (1971), Shor (1979)) with space stretching in the direction of difference of two adjacent subgradients is a competitive method of nonsmooth optimization. However, the original r-algorithm is designed to…

Optimization and Control · Mathematics 2023-11-08 Vladimir Norkin , Anton Kozyriev

Non-rigid 3D registration, which deforms a source 3D shape in a non-rigid way to align with a target 3D shape, is a classical problem in computer vision. Such problems can be challenging because of imperfect data (noise, outliers and…

Computer Vision and Pattern Recognition · Computer Science 2023-02-21 Yuxin Yao , Bailin Deng , Weiwei Xu , Juyong Zhang

Our work presents a new iterative scheme to approximate the fixed points of nonexpansive mapping. The proposed algorithm is constructed to enhance convergence efficiency while preserving theoretical robustness. Under appropriate assumptions…

Functional Analysis · Mathematics 2026-01-12 Nida Izhar Mallick , Izhar Uddin

Iterative Closest Point (ICP) is a widely used method for performing scan-matching and registration. Being simple and robust method, it is still computationally expensive and may be challenging to use in real-time applications with limited…

Robotics · Computer Science 2017-09-19 A. L. Pavlov , G. V. Ovchinnikov , D. Yu. Derbyshev , D. Tsetserukou , I. V. Oseledets

Due to the non-smoothness of optimization problems in Machine Learning, generalized smoothness assumptions have been gaining a lot of attention in recent years. One of the most popular assumptions of this type is $(L_0,L_1)$-smoothness…

Optimization and Control · Mathematics 2024-12-30 Eduard Gorbunov , Nazarii Tupitsa , Sayantan Choudhury , Alen Aliev , Peter Richtárik , Samuel Horváth , Martin Takáč

The alternating direction method of multipliers (ADMM) has been popular for solving many signal processing problems, convex or nonconvex. In this paper, we study an asynchronous implementation of the ADMM for solving a nonconvex nonsmooth…

Information Theory · Computer Science 2014-12-19 Mingyi Hong

We consider an unconstrained problem of minimizing a smooth convex function which is only available through noisy observations of its values, the noise consisting of two parts. Similar to stochastic optimization problems, the first part is…

Optimization and Control · Mathematics 2020-09-22 Eduard Gorbunov , Pavel Dvurechensky , Alexander Gasnikov

Anderson acceleration (AA) is a well-known method for accelerating the convergence of iterative algorithms, with applications in various fields including deep learning and optimization. Despite its popularity in these areas, the…

Machine Learning · Computer Science 2023-08-25 Sarwan Ali , Prakash Chourasia , Murray Patterson

Anderson Acceleration (AA) has been widely used to solve nonlinear fixed-point problems due to its rapid convergence. This work focuses on a variant of AA in which multiple Picard iterations are performed between each AA step, referred to…

Numerical Analysis · Mathematics 2025-07-15 Xue Feng , M. Paul Laiu , Thomas Strohmer

We analyze convergence rates of stochastic optimization procedures for non-smooth convex optimization problems. By combining randomized smoothing techniques with accelerated gradient methods, we obtain convergence rates of stochastic…

Optimization and Control · Mathematics 2012-04-10 John C. Duchi , Peter L. Bartlett , Martin J. Wainwright

We consider the problem of minimizing the sum of a smooth function $h$ with a bounded Hessian, and a nonsmooth function. We assume that the latter function is a composition of a proper closed function $P$ and a surjective linear map $\cal…

Optimization and Control · Mathematics 2015-11-17 Guoyin Li , Ting Kei Pong

The state-of-art seismic imaging techniques treat inversion tasks such as FWI and LSRTM as PDE-constrained optimization problems. Due to the large-scale nature, gradient-based optimization algorithms are preferred in practice to update the…

Numerical Analysis · Mathematics 2020-11-16 Yunan Yang

The Anderson Mixing (AM) method is a popular approach for accelerating fixed-point iterations by leveraging historical information from previous steps. In this paper, we introduce the Riemannian Anderson Mixing (RAM) method, an extension of…

Optimization and Control · Mathematics 2023-09-13 Zanyu Li , Chenglong Bao

We present new convolution based smooth approximations to the absolute value function and apply them to construct gradient based algorithms such as the nonlinear conjugate gradient scheme to obtain sparse, regularized solutions of linear…

Numerical Analysis · Mathematics 2015-07-02 Sergey Voronin , Gorkem Ozkaya , Davis Yoshida

We propose a proximal variable smoothing algorithm for a nonsmooth optimization problem whose cost function is the sum of three functions including a weakly convex composite function. The proposed algorithm has a single-loop structure…

Optimization and Control · Mathematics 2025-06-09 Keita Kume , Isao Yamada

In this paper, we consider a class of nonconvex and nonsmooth fractional programming problems, that involve the sum of a convex, possibly nonsmooth function composed with a linear operator and a differentiable, possibly nonconvex function…

Optimization and Control · Mathematics 2025-03-18 Radu Ioan Boţ , Guoyin Li , Min Tao

We provide rigorous theoretical bounds for Anderson acceleration (AA) that allow for approximate calculations when applied to solve linear problems. We show that, when the approximate calculations satisfy the provided error bounds, the…

Numerical Analysis · Mathematics 2024-04-30 Massimiliano Lupo Pasini , M. Paul Laiu

We analyze a modified version of Nesterov accelerated gradient algorithm, which applies to affine fixed point problems with non self-adjoint matrices, such as the ones appearing in the theory of Markov decision processes with discounted or…

Optimization and Control · Mathematics 2021-07-05 Marianne Akian , Stéphane Gaubert , Zheng Qu , Omar Saadi

In this paper, we consider the nonsmooth convex optimization problems over the fixed point constraint sets of firmly nonexpansive operators. To find an optimal solution of the problem, we present an iterative method based on the hybrid…

Optimization and Control · Mathematics 2026-03-23 Ontima Pankoon , Nimit Nimana , Yeol Je Cho

Recent studies have shown that many nonconvex machine learning problems satisfy a generalized-smooth condition that extends beyond traditional smooth nonconvex optimization. However, the existing algorithms are not fully adapted to such…

Optimization and Control · Mathematics 2025-10-03 Yufeng Yang , Erin Tripp , Yifan Sun , Shaofeng Zou , Yi Zhou