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.
This paper proposes a general line-search Newton framework for unconstrained optimization that avoids repeated Hessian regularization by exploiting the Newton direction only when it is well-defined and suitable and provides the first Newton-type algorithm together with a comprehensive convergence analysis for this impo...
This work can specifically ensure, without any smoothness assumptions, convergence to Mordukhovich stationarity as long as the base directions asymptotically revert to the negative gradient for small stepsizes.
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.
Empirical results reveal that VR-DR remains highly effective for nonsmooth loss functions, significantly broadening its practical utility beyond its theoretical constraints.
Zehui Jia, Deng-Hui Li, Zhiyu Liu et al.· Journal of Scientific Comput...· 0 citations
The quadratic optimization-free (QO-free) method is a class of powerful and effective algorithms for solving nonlinearly constrained optimization problems in Euclidean spaces. The aim of the present work is to extend this method to solve optimization problems on manifolds with additional equality and inequality constra...
Chun-Ming Tang, Hao He, Wen Huang et al.· 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...
