![](/images/graphics-bg.png)
A Cutting Plane and Level Stabilization Bundle Method with Inexact Data for Minimizing Nonsmooth Nonconvex Functions
Joint Authors
Source
Issue
Vol. 2014, Issue 2014 (31 Dec. 2014), pp.1-6, 6 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2014-04-13
Country of Publication
Egypt
No. of Pages
6
Main Subjects
Abstract EN
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.
American Psychological Association (APA)
Shen, Jie& Li, Dan& Pang, Li-Ping. 2014. A Cutting Plane and Level Stabilization Bundle Method with Inexact Data for Minimizing Nonsmooth Nonconvex Functions. Abstract and Applied Analysis،Vol. 2014, no. 2014, pp.1-6.
https://search.emarefa.net/detail/BIM-1013456
Modern Language Association (MLA)
Shen, Jie…[et al.]. A Cutting Plane and Level Stabilization Bundle Method with Inexact Data for Minimizing Nonsmooth Nonconvex Functions. Abstract and Applied Analysis No. 2014 (2014), pp.1-6.
https://search.emarefa.net/detail/BIM-1013456
American Medical Association (AMA)
Shen, Jie& Li, Dan& Pang, Li-Ping. A Cutting Plane and Level Stabilization Bundle Method with Inexact Data for Minimizing Nonsmooth Nonconvex Functions. Abstract and Applied Analysis. 2014. Vol. 2014, no. 2014, pp.1-6.
https://search.emarefa.net/detail/BIM-1013456
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1013456