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Error Bounds and Finite Termination for Constrained Optimization Problems
Joint Authors
Song, Daojin
Liu, Bingzhuang
Zhao, Wenling
Source
Mathematical Problems in Engineering
Issue
Vol. 2014, Issue 2014 (31 Dec. 2014), pp.1-10, 10 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2014-04-30
Country of Publication
Egypt
No. of Pages
10
Main Subjects
Abstract EN
We present a global error bound for the projected gradient of nonconvex constrained optimization problems and a local error bound for the distance from a feasible solution to the optimal solution set of convex constrained optimization problems, by using the merit function involved in the sequential quadratic programming (SQP) method.
For the solution sets (stationary points set and KKT points set) of nonconvex constrained optimization problems, we establish the definitions of generalized nondegeneration and generalized weak sharp minima.
Based on the above, the necessary and sufficient conditions for a feasible solution of the nonconvex constrained optimization problems to terminate finitely at the two solutions are given, respectively.
Accordingly, the results in this paper improve and popularize existing results known in the literature.
Further, we utilize the global error bound for the projected gradient with the merit function being computed easily to describe these necessary and sufficient conditions.
American Psychological Association (APA)
Zhao, Wenling& Song, Daojin& Liu, Bingzhuang. 2014. Error Bounds and Finite Termination for Constrained Optimization Problems. Mathematical Problems in Engineering،Vol. 2014, no. 2014, pp.1-10.
https://search.emarefa.net/detail/BIM-450511
Modern Language Association (MLA)
Zhao, Wenling…[et al.]. Error Bounds and Finite Termination for Constrained Optimization Problems. Mathematical Problems in Engineering No. 2014 (2014), pp.1-10.
https://search.emarefa.net/detail/BIM-450511
American Medical Association (AMA)
Zhao, Wenling& Song, Daojin& Liu, Bingzhuang. Error Bounds and Finite Termination for Constrained Optimization Problems. Mathematical Problems in Engineering. 2014. Vol. 2014, no. 2014, pp.1-10.
https://search.emarefa.net/detail/BIM-450511
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-450511