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This paper proposes a novel stochastic version of damped and regularized BFGS method for addressing the above problems.

Numerical Analysis · Mathematics 2019-12-11 H. Chen , H. C. Wu , S. C. Chan , W. H. Lam

We introduce a framework for quasi-Newton forward--backward splitting algorithms (proximal quasi-Newton methods) with a metric induced by diagonal $\pm$ rank-$r$ symmetric positive definite matrices. This special type of metric allows for a…

Optimization and Control · Mathematics 2018-11-27 Stephen Becker , Jalal Fadili , Peter Ochs

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

Minimax problems have gained tremendous attentions across the optimization and machine learning community recently. In this paper, we introduce a new quasi-Newton method for minimax problems, which we call $J$-symmetric quasi-Newton method.…

Optimization and Control · Mathematics 2023-01-20 Azam Asl , Haihao Lu , Jinwen Yang

In this paper, we study the application of quasi-Newton methods for solving empirical risk minimization (ERM) problems defined over a large dataset. Traditional deterministic and stochastic quasi-Newton methods can be executed to solve such…

Optimization and Control · Mathematics 2021-10-28 Qiujiang Jin , Aryan Mokhtari

Classical theory for quasi-Newton schemes has focused on smooth deterministic unconstrained optimization while recent forays into stochastic convex optimization have largely resided in smooth, unconstrained, and strongly convex regimes.…

Optimization and Control · Mathematics 2020-11-03 Afrooz Jalilzadeh , Angelia Nedich , Uday V. Shanbhag , Farzad Yousefian

Solving an optimization problem whose objective function is the sum of two convex functions has received considerable interests in the context of image processing recently. In particular, we are interested in the scenario when a…

Computer Vision and Pattern Recognition · Computer Science 2014-12-16 Dai-Qiang Chen

In recent years, various subspace algorithms have been developed to handle large-scale optimization problems. Although existing subspace Newton methods require fewer iterations to converge in practice, the matrix operations and full…

Optimization and Control · Mathematics 2024-06-05 Taisei Miyaishi , Ryota Nozawa , Pierre-Louis Poirion , Akiko Takeda

A new and simple method for quasi-convex optimization is introduced from which its various applications can be derived. Especially, a global optimum under constrains can be approximated for all continuous functions.

Optimization and Control · Mathematics 2020-12-07 Sompong Dhompongsa , Poom Kumam

In this paper we present a novel quasi-Newton algorithm for use in stochastic optimisation. Quasi-Newton methods have had an enormous impact on deterministic optimisation problems because they afford rapid convergence and computationally…

Systems and Control · Electrical Eng. & Systems 2019-09-04 Adrian Wills , Thomas Schön

A quasi-Newton method with cubic regularization is designed for solving Riemannian unconstrained nonconvex optimization problems. The proposed algorithm is fully adaptive with at most ${\cal O} (\epsilon_g^{-3/2})$ iterations to achieve a…

Optimization and Control · Mathematics 2024-02-21 Mauricio S. Louzeiro , Gilson N. Silva , Jinyun Yuan , Daoping Zhang

In this paper, we propose an accelerated quasi-Newton proximal extragradient (A-QPNE) method for solving unconstrained smooth convex optimization problems. With access only to the gradients of the objective, we prove that our method can…

Optimization and Control · Mathematics 2023-06-06 Ruichen Jiang , Aryan Mokhtari

In this paper, we introduce a quasi-Newton method optimized for efficiently solving quasi-linear elliptic equations and systems, with a specific focus on GPU-based computation. By approximating the Jacobian matrix with a combination of…

Numerical Analysis · Mathematics 2025-03-25 Wenrui Hao , Sun Lee , Xiangxiong Zhang

We propose a globally convergent Gauss-Newton algorithm for finding a local optimal solution of a non-convex and possibly non-smooth optimization problem. The algorithm that we present is based on a Gauss-Newton-type iteration for the…

Optimization and Control · Mathematics 2020-12-08 Ilyes Mezghani , Quoc Tran-Dinh , Ion Necoara , Anthony Papavasiliou

This work presents a novel version of recently developed Gauss-Newton method for solving systems of nonlinear equations, based on upper bound of solution residual and quadratic regularization ideas. We obtained for such method global…

Optimization and Control · Mathematics 2021-05-04 Nikita Yudin , Alexander Gasnikov

In this paper, we propose a globally convergent method for solving constrained nonlinear systems. The method combines an efficient Newton conditional gradient method with a derivative-free and nonmonotone linesearch strategy. The global…

Optimization and Control · Mathematics 2018-06-06 M. L. N. Gonçalves , F. R. Oliveira

A q-Gauss-Newton algorithm is an iterative procedure that solves nonlinear unconstrained optimization problems based on minimization of the sum squared errors of the objective function residuals. Main advantage of the algorithm is that it…

Optimization and Control · Mathematics 2021-05-28 Danijela Protic , Miomir Stankovic

Many practical optimization problems involve objective function values that are corrupted by unavoidable numerical errors. In smooth nonconvex optimization, quasi-Newton methods combined with line search are widely used due to their…

Optimization and Control · Mathematics 2026-03-12 Hiroki Hamaguchi , Naoki Marumo , Akiko Takeda

This paper is devoted to studying the global and finite convergence of the semi-smooth Newton method for solving a piecewise linear system that arises in cone-constrained quadratic programming problems and absolute value equations. We first…

Optimization and Control · Mathematics 2023-01-24 Nicolas F. Armijo , Yunier Bello-Cruz , Gabriel Haeser

We propose a quasi-Newton-type method for nonconvex optimization with Lipschitz continuous gradients and Hessians. The algorithm finds an $\varepsilon$-stationary point within $\tilde{\mathrm{O}}(d^{1/4} \varepsilon^{-13/8})$ gradient…

Optimization and Control · Mathematics 2025-12-11 Naoki Marumo