English
Related papers

Related papers: Scalable adaptive cubic regularization methods

200 papers

Randomized iterative algorithms for solving a factorized linear system, $\mathbf A\mathbf B\mathbf x=\mathbf b$ with $\mathbf A\in{\mathbb{R}}^{m\times \ell}$, $\mathbf B\in{\mathbb{R}}^{\ell\times n}$, and $\mathbf b\in{\mathbb{R}}^m$,…

Numerical Analysis · Mathematics 2023-07-25 Kui Du

In this paper, we study the Crank-Nicolson method for temporal dimension and the piecewise quadratic polynomial collocation method for spatial dimensions of time-dependent nonlocal problems. The new theoretical results of such…

Numerical Analysis · Mathematics 2020-06-30 Rongjun Cao , Minghua Chen , Michael K. Ng , Yu-Jiang Wu

Bayes linear analysis and approximate Bayesian computation (ABC) are techniques commonly used in the Bayesian analysis of complex models. In this article we connect these ideas by demonstrating that regression-adjustment ABC algorithms…

Methodology · Statistics 2012-12-10 D. J. Nott , Y. Fan , L. Marshall , S. A. Sisson

In this paper we present a method for the regularized solution of nonlinear inverse problems, based on Ivanov regularization (also called method of quasi solutions or constrained least squares regularization). This leads to the minimization…

Numerical Analysis · Mathematics 2015-09-11 Barbara Kaltenbacher , Franz Rendl , Elena Resmerita

BJT-based 2D temperature-sensor arrays are factory-calibrated to +/-0.1 degC, but post-deployment thermal and mechanical stresses drift their per-sensor gain-offset parameters by an order of magnitude, and in-lab recalibration is…

Distributed, Parallel, and Cluster Computing · Computer Science 2026-05-26 Yinglei Ma , Fei Xiao

A coarse grid correction (CGC) approach is proposed to enhance the efficiency of the matrix exponential and $\varphi$ matrix function evaluations. The approach is intended for iterative methods computing the matrix-vector products with…

Numerical Analysis · Mathematics 2024-04-23 Mike A. Botchev

For many applications involving a sequence of linear systems with slowly changing system matrices, subspace recycling, which exploits relationships among systems and reuses search space information, can achieve huge gains in iterations…

Numerical Analysis · Mathematics 2023-06-28 Misha E. Kilmer , Eric de Sturler

This paper introduces a robust and computationally efficient estimation framework for high-dimensional volatility models in the BEKK-ARCH class. The proposed approach employs data truncation to ensure robustness against heavy-tailed…

Statistics Theory · Mathematics 2026-05-26 Kejun Chen , Yuchang Lin , Qianqian Zhu

Successive quadratic approximations, or second-order proximal methods, are useful for minimizing functions that are a sum of a smooth part and a convex, possibly nonsmooth part that promotes regularization. Most analyses of iteration…

Optimization and Control · Mathematics 2019-01-25 Ching-pei Lee , Stephen J. Wright

The augmented Lagrangian method (ALM) is a benchmark for convex programming problems with linear constraints; ALM and its variants for linearly equality-constrained convex minimization models have been well studied in the literature.…

Optimization and Control · Mathematics 2022-06-22 Bingsheng He , Shengjie Xu , Jing Yuan

Accurate value estimates are important for off-policy reinforcement learning. Algorithms based on temporal difference learning typically are prone to an over- or underestimation bias building up over time. In this paper, we propose a…

Machine Learning · Computer Science 2022-10-24 Nicolai Dorka , Tim Welschehold , Joschka Boedecker , Wolfram Burgard

This paper presents strong worst-case iteration and operation complexity guarantees for Riemannian adaptive regularized Newton methods, a unified framework encompassing both Riemannian adaptive regularization (RAR) methods and Riemannian…

Optimization and Control · Mathematics 2025-05-14 Chenyu Zhang , Rujun Jiang

This paper presents a centralized predictive cost adaptive control (PCAC) strategy for the position and attitude control of quadrotors. PCAC is an optimal, prediction-based control method that uses recursive least squares (RLS) to identify…

Systems and Control · Electrical Eng. & Systems 2025-08-26 Tam W. Nguyen

This paper focuses on regularisation methods using models up to the third order to search for up to second-order critical points of a finite-sum minimisation problem. The variant presented belongs to the framework of [3]: it employs random…

Numerical Analysis · Mathematics 2021-04-05 Stefania Bellavia , Gianmarco Gurioli , Benedetta Morini , Philippe L. Toint

We propose an adaptive refinement algorithm to solve total variation regularized measure optimization problems. The method iteratively constructs dyadic partitions of the unit cube based on i) the resolution of discretized dual problems and…

Optimization and Control · Mathematics 2023-01-19 Axel Flinth , Frédéric de Gournay , Pierre Weiss

Reliable uncertainty quantification is essential for deploying machine learning systems in high-stakes domains. Conformal prediction provides distribution-free coverage guarantees but often produces overly large prediction sets, limiting…

Machine Learning · Computer Science 2026-04-28 Yunpeng Xu , Wenge Guo , Zhi Wei

We propose a fully-corrective generalized conditional gradient method (FC-GCG) for the minimization of the sum of a smooth, convex loss function and a convex one-homogeneous regularizer over a Banach space. The algorithm relies on the…

Optimization and Control · Mathematics 2023-07-17 Kristian Bredies , Marcello Carioni , Silvio Fanzon , Daniel Walter

This paper introduces an innovative singularity-free output feedback model reference adaptive control (MRAC) method applicable to a wide range of continuous-time linear time-invariant (LTI) systems with general relative degrees. Unlike…

Systems and Control · Electrical Eng. & Systems 2024-11-05 Zhipeng Zhang , Yanjun Zhang , Jian Sun

The trust-region (TR) method is renowned historically for its robustness in nonconvex problems and extraordinary numerical performance, but the study of its performance in convex optimization is somehow limited. This paper complements the…

Optimization and Control · Mathematics 2026-01-26 Yuntian Jiang , Chang He , Chuwen Zhang , Dongdong Ge , Bo Jiang , Yinyu Ye

We present a random-subspace variant of cubic regularization algorithm that chooses the size of the subspace adaptively, based on the rank of the projected second derivative matrix. Iteratively, our variant only requires access to…

Optimization and Control · Mathematics 2025-01-09 Edward Tansley , Coralia Cartis