Miantao Chao – Optimization Online

Newtonian Methods with Wolfe Linesearch in Nonsmooth Optimization and Machine Learning

Published: 2025/01/31

Nonlinear Optimization Lasso problems, machine learning, nonsmooth Newton methods, nonsmooth optimization, support vector machines, variational analysis, Wolfe linesearch

This paper introduces and develops coderivative-based Newton methods with Wolfe linesearch conditions to solve various classes of problems in nonsmooth optimization and machine learning. We first propose a generalized regularized Newton method with Wolfe linesearch (GRNM-W) for unconstrained $C^{1,1}$ minimization problems (which are second-order nonsmooth) and establish global as well as local superlinear convergence of … Read more

A descent method for nonsmooth multiobjective optimization problems on Riemannian manifolds

Published: 2023/04/24

Constrained Nonlinear Optimization, Nonlinear Optimization, Nonsmooth Optimization Multiobjective optimization · Riemannian manifolds · Descent method · Pareto optimality · Convergence analysis

In this paper, a descent method for nonsmooth multiobjective optimization problems on complete Riemannian manifolds is proposed. The objective functions are only assumed to be locally Lipschitz continuous instead of convexity used in existing methods. A necessary condition for Pareto optimality in Euclidean space is generalized to the Riemannian setting. At every iteration, an acceptable … Read more