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Preprint Aug 2026

A Local-Linearly Convergent Algorithm for Nonconvex Equality-Constrained Optimization

For solving nonconvex equality-constrained optimization problems, a recent Gradient-Eigenstep Algorithm by Goyens et al.~is an iteration-efficient approach, based on minimizing Fletcher's augmented Lagrangian function, for finding an approximate second-order stationary point from an arbitrary starting point. In this pa...

F. Curtis, Ling-Jun Guo, Daniel P. Robinson · 0 citations
Preprint Aug 2026

Adaptive Barzilai-Borwein Proximal Gradient Method for Nonconvex Optimization

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...

Yi-Nuo Li, Na Huang, Ruizhi Zhou · 0 citations
Sep 2026

A HYBRID ADAPTIVE RESTART FRAMEWORK FOR ACCELERATED INEXACT PROXIMAL GRADIENT METHODS IN NON-CONVEX OPTIMIZATION

Accelerated inexact proximal-gradient methods are effective for non-convex composite optimization, but combining adaptive step sizes with acceleration can lead to numerical instability. We propose a Hybrid Adaptive Accelerated Inexact Proximal Gradient (HA-AIPG) framework designed to balance exploratory steps with conv...

Nontawat Eiamniran, P. Cholamjiak, Jen-Chih Yao · 0 citations

Global convergence of a coderivative-based regularized Newton method with damping for nonsmooth optimization

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.

Wei Ouyang, Zhenghong Tan, JiangxingZhu · 0 citations
Preprint Sep 2026

Projected Subgradient Methods for a Class of Nonsmooth and Nonconvex Optimization Problems

We investigate the optimization problem of minimizing a nonsmooth function that satisfies a nonsmooth version of the descent lemma over a nonempty and closed but not necessarily convex set. The objective function belongs to the class of upper-$\mathcal{C}^2$ functions, whereas the constraints may promote a sparse or lo...

Christian Kanzow, Jannis Krüger, Leo Lehmann · 0 citations
Aug 2026

Stochastic ADMM with Balanced Augmented Lagrangian Method for Nonconvex and Nonsmooth Finite-Sum Optimization

In this paper, we propose a balanced augmented Lagrangian method based on accelerated stochastic ADMM (b-ASADMM) to efficiently solve structured separable nonconvex optimization problems subject to linear constraints. The objective function in this problem comprises potentially nonsmooth and smooth functions, where the...

Qiaoling Zhang, Chuang Yang, Hu Shao · 0 citations

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