non-lipschitz – Optimization Online

A Riemannian smoothing steepest descent method for non-Lipschitz optimization on submanifolds

Published: 2021/04/09

Nonlinear Optimization non-lipschitz, riemannian generalized subdifferentials, riemannian gradient sub-consistency, riemannian submanifold, smoothing steepest descent method

In this paper, we propose a Riemannian smoothing steepest descent method to minimize a nonconvex and non-Lipschitz function on submanifolds. The generalized subdifferentials on Riemannian manifold and the Riemannian gradient sub-consistency are defined and discussed. We prove that any accumulation point of the sequence generated by the Riemannian smoothing steepest descent method is a stationary … Read more

Partially separable convexly-constrained optimization with non-Lipschitz singularities and its complexity

Published: 2017/04/20

Xiaojun Chen

Philippe L. Toint

Hong Wang

Nonsmooth Optimization complexity, non-lipschitz, nonlinear optimization

An adaptive regularization algorithm using high-order models is proposed for partially separable convexly constrained nonlinear optimization problems whose objective function contains non-Lipschitzian $\ell_q$-norm regularization terms for $q\in (0,1)$. It is shown that the algorithm using an $p$-th order Taylor model for $p$ odd needs in general at most $O(\epsilon^{-(p+1)/p})$ evaluations of the objective function and … Read more