Well-Posedness and Primal-Dual Analysis of Some Convex Separable Optimization Problems
Author
Source
Advances in Operations Research
Issue
Vol. 2013, Issue 2013 (31 Dec. 2013), pp.1-10, 10 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2013-04-15
Country of Publication
Egypt
No. of Pages
10
Main Subjects
Engineering Sciences and Information Technology
Topics
Abstract EN
We focus on some convex separable optimization problems, considered by the author in previous papers, for which problems, necessary and sufficient conditions or sufficient conditions have been proved, and convergent algorithms of polynomial computational complexity have been proposed for solving these problems.
The concepts of well-posedness of optimization problems in the sense of Tychonov, Hadamard, and in a generalized sense, as well as calmness in the sense of Clarke, are discussed.
It is shown that the convex separable optimization problems under consideration are calm in the sense of Clarke.
The concept of stability of the set of saddle points of the Lagrangian in the sense of Gol'shtein is also discussed, and it is shown that this set is not stable for the “classical” Lagrangian.
However, it turns out that despite this instability, due to the specificity of the approach, suggested by the author for solving problems under consideration, it is not necessary to use modified Lagrangians but only the “classical” Lagrangians.
Also, a primal-dual analysis for problems under consideration in view of methods for solving them is presented.
American Psychological Association (APA)
Stefanov, Stefan M.. 2013. Well-Posedness and Primal-Dual Analysis of Some Convex Separable Optimization Problems. Advances in Operations Research،Vol. 2013, no. 2013, pp.1-10.
https://search.emarefa.net/detail/BIM-459791
Modern Language Association (MLA)
Stefanov, Stefan M.. Well-Posedness and Primal-Dual Analysis of Some Convex Separable Optimization Problems. Advances in Operations Research No. 2013 (2013), pp.1-10.
https://search.emarefa.net/detail/BIM-459791
American Medical Association (AMA)
Stefanov, Stefan M.. Well-Posedness and Primal-Dual Analysis of Some Convex Separable Optimization Problems. Advances in Operations Research. 2013. Vol. 2013, no. 2013, pp.1-10.
https://search.emarefa.net/detail/BIM-459791
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-459791