Aug 2026· Discover Computing· Vol 29· 0 citations· 29 references
Abstract
The Barzilai and Borwein methods are renowned for their simplicity and numerical efficiency, attracting significant attention for large-scale optimization problems. Recently, a new adaptive Barzilai and Borwein method with a nonmonotone line search has been proposed for general unconstrained optimization. Building on this approach, we propose, analyze and test an adaptive Barzilai and Borwein method to solve systems of nonlinear equations with convex constraints, incorporating a hyperplane projection technique. The proposed method has several attractive properties, including not requiring Jacobian information and avoiding matrix storage per iteration. Under standard assumptions, the global convergence of the proposed method is established. Finally, numerical experiments are presented to demonstrate the practical performance of the proposed method.
The proposed AdaBBNC incorporates a flexible BB-based curvature estimate into the proximal gradient framework to enhance adaptability in nonconvex settings and achieves the optimal iteration complexity of $\mathcal{O}(\epsilon^{-2})$ for finding an $\epsilon$-stationary point, without requiring any prior knowledge of t...
This work proposes to integrate the importance sampling strategy with mini-batch techniques into the SARAH framework, developing a variant termed SARAH-MI-RBB, which outperforms existing state-of-the-art methods in its class.
Lei Liu, Hai-Lin Sun, Dan Xue· Asia-Pacific Journal of Oper...· 0 citations
The results show that the proposed Wolfe-type spectral conjugate gradient method performs competitively overall, matching or outperforming existing methods on most problems tested, while a few specific limitations of the current implementation are also identified and discussed.
This study presents a spectral convex combination modification of the Liu Storey method for unconstrained optimization, aiming to enhance efficiency and adaptability compared to existing approaches.
Muhammad Aqiil Iqmal Ishak, Nurfaqiha Abu Salim, S. M. Marjugi· Applied mathematics and comp...· 0 citations
A globally convergent regularized Newton method with positive definite regularization for solving nonsmooth optimization problems that replaces the identity matrix in traditional algorithms with a general positive-definite symmetric matrix to regularize the generalized Hessian.
Newton-type algorithms are among the most effective methods for solving optimization problems because of their rapid local convergence. However, extending these methods to nonsmooth optimization is challenging due to the difficulty of incorporating second-order information. To address this issue, we propose a coderivat...
Sina Kazemdehbashi, Yan-Chao Liu, Boris S. Mordukhovich· 0 citations
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