- Minimization of nonsmooth nonconvex functions using inexact evaluations and its worst-case complexity Serge Gratton(serge.grattonenseeiht.fr) Ehouarn Simon(ehouarn.simonenseeiht.fr) Philippe L. Toint(philippe.tointunamur.be) Abstract: An adaptive regularization algorithm using inexact function and derivatives evaluations is proposed for the solution of composite nonsmooth nonconvex optimization. It is shown that this algorithm needs at most O(|log(epsilon)|.epsilon^{-2}) evaluations of the problem's functions and their derivatives for finding an $\epsilon$-approximate first-order stationary point. This complexity bound therefore generalizes that provided by [Bellavia, Gurioli, Morini and Toint, 2018] for inexact methods for smooth nonconvex problems, and is within a factor |log(epsilon)| of the optimal bound known for smooth and nonsmooth nonconvex minimization with exact evaluations. A practically more restrictive variant of the algorithm with worst-case complexity O(|log(epsilon)|+epsilon^{-2}) is also presented. Keywords: evaluation complexity, nonsmooth problems, nonconvex optimization, composite functions, inexact evaluations Category 1: Nonlinear Optimization (Unconstrained Optimization ) Category 2: Nonlinear Optimization (Constrained Nonlinear Optimization ) Category 3: Convex and Nonsmooth Optimization (Nonsmooth Optimization ) Citation: Download: [PDF]Entry Submitted: 02/27/2019Entry Accepted: 02/27/2019Entry Last Modified: 02/27/2019Modify/Update this entry Visitors Authors More about us Links Subscribe, Unsubscribe Digest Archive Search, Browse the Repository Submit Update Policies Coordinator's Board Classification Scheme Credits Give us feedback Optimization Journals, Sites, Societies Optimization Online is supported by the Mathematical Optmization Society.