A cutting plane and level stabilization bundle method with inexact data for minimizing nonsmooth nonconvex functions
type: Item
instance of: scholarly article
title: A cutting plane and level stabilization bundle method with inexact data for minimizing nonsmooth nonconvex functions
zbMATH Open document ID: 1470.90160
DOI: 10.1155/2014/192893
author: Jie Shen
author: Dan Li
author: Li-Ping Pang
published in: Abstract and Applied Analysis
publication date: 2019-02-14T00:00:00Z
review text: Summary: Under the condition that the values of the objective function and its subgradient are computed approximately, we introduce a cutting plane and level bundle method for minimizing nonsmooth nonconvex functions by combining cutting plane method with the ideas of proximity control and level constraint. The proposed algorithm is based on the construction of both a lower and an upper polyhedral approximation model to the objective function and calculates new iteration points by solving a subproblem in which the model is employed not only in the objective function but also in the constraints. Compared with other proximal bundle methods, the new variant updates the lower bound of the optimal value, providing an additional useful stopping test based on the optimality gap. Another merit is that our algorithm makes a distinction between affine pieces that exhibit a convex or a concave behavior relative to the current iterate. Convergence to some kind of stationarity point is proved under some looser conditions.
Mathematics Subject Classification ID: 90C56
Mathematics Subject Classification ID: 90C26
Mathematics Subject Classification ID: 90C25
zbMATH DE Number: 7021909
Wikidata QID: Q59035940
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2014/192893
OpenAlex ID: W2164284121
cites work: Newton's method for convex programming and Tschebyscheff approximation
cites work: The Cutting-Plane Method for Solving Convex Programs
cites work: Minimizing Nonconvex Nonsmooth Functions via Cutting Planes and Proximity Control
cites work: New variants of bundle methods
cites work: A doubly stabilized bundle method for nonsmooth convex optimization
cites work: A proximal bundle method based on approximate subgradients
cites work: Optimization and nonsmooth analysis
cites work: Optimization of lipschitz continuous functions
cites work: A Dual Method for Certain Positive Semidefinite Quadratic Programming Problems
cites work: Tuning strategy for the proximity parameter in convex minimization
description: scientific article; zbMATH DE number 7021909