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Reseach Article

Finite Termination by using the Asymptotic Dual for Dynamic Bundle Method

Published on February 2013 by Paras Bhatnagar, Shipra Kaushik, Ashok Kumar Vasishtha
International Conference on Advances in Computer Application 2013
Foundation of Computer Science USA
ICACA2013 - Number 1
February 2013
Authors: Paras Bhatnagar, Shipra Kaushik, Ashok Kumar Vasishtha
874cd2e8-00ae-4f0d-a329-8ec069c3f286

Paras Bhatnagar, Shipra Kaushik, Ashok Kumar Vasishtha . Finite Termination by using the Asymptotic Dual for Dynamic Bundle Method. International Conference on Advances in Computer Application 2013. ICACA2013, 1 (February 2013), 28-29.

@article{
author = { Paras Bhatnagar, Shipra Kaushik, Ashok Kumar Vasishtha },
title = { Finite Termination by using the Asymptotic Dual for Dynamic Bundle Method },
journal = { International Conference on Advances in Computer Application 2013 },
issue_date = { February 2013 },
volume = { ICACA2013 },
number = { 1 },
month = { February },
year = { 2013 },
issn = 0975-8887,
pages = { 28-29 },
numpages = 2,
url = { /proceedings/icaca2013/number1/10392-1008/ },
publisher = {Foundation of Computer Science (FCS), NY, USA},
address = {New York, USA}
}
%0 Proceeding Article
%1 International Conference on Advances in Computer Application 2013
%A Paras Bhatnagar
%A Shipra Kaushik
%A Ashok Kumar Vasishtha
%T Finite Termination by using the Asymptotic Dual for Dynamic Bundle Method
%J International Conference on Advances in Computer Application 2013
%@ 0975-8887
%V ICACA2013
%N 1
%P 28-29
%D 2013
%I International Journal of Computer Applications
Abstract

This research paper deals with the question of finite termination of the Algorithm for Dynamic bundle method. For a polyhedral dual function f , if the stopping parameter is set to tol = 0, and the bundle management is either "no bundle deletion" or "bundle selection", we provide a positive answer for that question.

References
  1. Kiwiel K. C. . Methods of descent for nondifferentiable optimization. Springer-Verlag, Berlin, 1985.
  2. Kiwiel K. C. . Exact penalty functions in proximal bundle methods for constrained convex nondifferentiable minimization. Math. Programming, 52(2, Ser. B):285–302, 1991.
  3. Kiwiel K. C. Approximations in Proximal Bundle Methods and Decomposition of Convex Programs. Journal of Optimization Theory and Applications, 84:529–548, 1995.
  4. Kiwiel K. C. . A proximal bundle method with approximate subgradient lineariza-tions. SIAM J. Optim. , 16:1007–1023, 2006.
  5. Lucena A. and Beasley J. E. . Branch and cut algorithms. In Advances in linear and integer programming, volume 4 of Oxford Lecture Ser. Math. Appl. , pages 187–221. Oxford Univ. Press, New York, 1996.
  6. Lemar´echal C. , Nemirovskii A. , and Nesterov Yu. . New variants of bundle methods. Math. Program. , 69:111–148, 1995.
  7. Lucena A. . Steiner problem in graphs: Lagrangean relaxation and cutting-planes. COAL Bulletin, 21(2):2–8, 1992. san and J. Vl.
  8. Luk. cek L. . A bundle-Newton method for nonsmooth unconstrained minimization. Math. Programming, 83(3, Ser. A):373–391, 1998.
Index Terms

Computer Science
Information Sciences

Keywords

Polyhedral Dual Function Dynamic Bundle Method Minimization Problem