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A new continuous regularized Gauss-Newton-type method with simultaneous updates of the operator $(F^{\pr*}(x(t))F'(x(t))+\ep(t) I)^{-1}$ for solving nonlinear ill-posed equations in a Hilbert space is proposed. A convergence theorem is…

Mathematical Physics · Physics 2007-05-23 Alexander G. Ramm , Alexandra B. Smirnova

The $p$-regularized subproblem (p-RS) is a regularisation technique in computing a Newton-like step for unconstrained optimization, which globally minimizes a local quadratic approximation of the objective function while incorporating with…

Optimization and Control · Mathematics 2018-05-01 Yong Hsia , Ruey-Lin Sheu , Ya-xiang Yuan

We extend the convergence analysis of the Scholtes-type regularization method for cardinality-constrained optimization problems. Its behavior is clarified in the vicinity of saddle points, and not just of minimizers as it has been done in…

Optimization and Control · Mathematics 2023-01-02 Sebastian Lammel , Vladimir Shikhman

In this paper, we present a dynamic non-diagonal regularization for interior point methods. The non-diagonal aspect of this regularization is implicit, since all the off-diagonal elements of the regularization matrices are cancelled out by…

Optimization and Control · Mathematics 2019-02-19 Spyridon Pougkakiotis , Jacek Gondzio

Stochastic convex optimization problems with nonlinear functional constraints are ubiquitous in signal processing applications including constrained least-squares, set-membership adaptive filtering, and trajectory optimization under…

Optimization and Control · Mathematics 2025-12-16 Panchajanya Sanyal , Srujan Teja Thomdapu , Ketan Rajawat

We study an iterative regularization method of optimal control problems with control constraints. The regularization method is based on generalized Bregman distances. We provide convergence results under a combination of a source condition…

Optimization and Control · Mathematics 2016-11-04 Frank Pörner , Daniel Wachsmuth

There has been growing interest in high-order tensor methods for nonconvex optimization, with adaptive regularization, as they possess better/optimal worst-case evaluation complexity globally and faster convergence asymptotically. These…

Optimization and Control · Mathematics 2025-01-17 Coralia Cartis , Wenqi Zhu

We adapt the quasi-monotone method from [2] for composite convex minimization in the stochastic setting. For the proposed numerical scheme we derive the optimal convergence rate in terms of the last iterate, rather than on average as it is…

Optimization and Control · Mathematics 2021-07-09 Vyacheslav Kungurtsev , Vladimir Shikhman

Equivariance is a powerful inductive bias in neural networks, improving generalisation and physical consistency. Recently, however, non-equivariant models have regained attention, due to their better runtime performance and imperfect…

Machine Learning · Computer Science 2026-05-27 Torben Berndt , Jan Stühmer

Applying half-quadratic optimization to loss functions can yield the corresponding regularizers, while these regularizers are usually not sparsity-inducing regularizers (SIRs). To solve this problem, we devise a framework to generate an SIR…

Optimization and Control · Mathematics 2023-10-10 Zhi-Yong Wang , Hing Cheung So

This paper focuses on the regularization of backward time-fractional diffusion problem on unbounded domain. This problem is well-known to be ill-posed, whence the need of a regularization method in order to recover stable approximate…

Numerical Analysis · Mathematics 2022-01-03 Walter Simo Tao Lee

Sequential quadratic optimization algorithms are proposed for solving smooth nonlinear optimization problems with equality constraints. The main focus is an algorithm proposed for the case when the constraint functions are deterministic,…

Optimization and Control · Mathematics 2020-07-22 Albert Berahas , Frank E. Curtis , Daniel P. Robinson , Baoyu Zhou

We consider trust-region methods for solving optimization problems where the objective is the sum of a smooth, nonconvex function and a nonsmooth, convex regularizer. We extend the global convergence theory of such methods to include…

Optimization and Control · Mathematics 2025-01-10 Minh N. Dao , Hung M. Phan , Lindon Roberts

In this article we develop and analyze novel iterative regularization techniques for the solution of systems of nonlinear ill--posed operator equations. The basic idea consists in considering separately each equation of this system and…

Numerical Analysis · Mathematics 2020-11-20 M. Haltmeier , A. Leitao , O. Scherzer

Computing the regularized solution of Bayesian linear inverse problems as well as the corresponding regularization parameter is highly desirable in many applications. This paper proposes a novel iterative method, termed the Projected Newton…

Numerical Analysis · Mathematics 2025-04-08 Haibo Li

Quantization is a widely used technique to compress and accelerate deep neural networks. However, conventional quantization methods use the same bit-width for all (or most of) the layers, which often suffer significant accuracy degradation…

Computer Vision and Pattern Recognition · Computer Science 2021-10-14 Weihan Chen , Peisong Wang , Jian Cheng

This paper describes a new approach on optimization of constraint satisfaction problems (CSPs) by means of substituting sub-CSPs with locally consistent regular membership constraints. The purpose of this approach is to reduce the number of…

Artificial Intelligence · Computer Science 2019-08-19 Sven Löffler , Ke Liu , Petra Hofstedt

In this paper, we propose two regularized proximal quasi-Newton methods with symmetric rank-1 update of the metric (SR1 quasi-Newton) to solve non-smooth convex additive composite problems. Both algorithms avoid using line search or other…

Optimization and Control · Mathematics 2024-11-22 Shida Wang , Jalal Fadili , Peter Ochs

Trace norm regularization is a widely used approach for learning low rank matrices. A standard optimization strategy is based on formulating the problem as one of low rank matrix factorization which, however, leads to a non-convex problem.…

Machine Learning · Computer Science 2017-08-01 Carlo Ciliberto , Dimitris Stamos , Massimiliano Pontil

This paper focuses on the minimization of a sum of a twice continuously differentiable function $f$ and a nonsmooth convex function. An inexact regularized proximal Newton method is proposed by an approximation to the Hessian of $f$…

Optimization and Control · Mathematics 2023-11-09 Ruyu Liu , Shaohua Pan , Yuqia Wu , Xiaoqi Yang