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
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...
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· Journal of Decision Making a...· 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.
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
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...