On the rate of convergence of sequential unconstrained minimization techniques

Ch. Großmann; A. A. Kaplan

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (1983)

  • Volume: 17, Issue: 3, page 267-292
  • ISSN: 0764-583X

How to cite

top

Großmann, Ch., and Kaplan, A. A.. "On the rate of convergence of sequential unconstrained minimization techniques." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 17.3 (1983): 267-292. <http://eudml.org/doc/193418>.

@article{Großmann1983,
author = {Großmann, Ch., Kaplan, A. A.},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {rate of convergence; sequential unconstrained minimization techniques; SUMT; comparison problems; penalty methods; convergence bounds; quasi- barrier method; parameter selection rules; regularized techniques; methods of centers},
language = {eng},
number = {3},
pages = {267-292},
publisher = {Dunod},
title = {On the rate of convergence of sequential unconstrained minimization techniques},
url = {http://eudml.org/doc/193418},
volume = {17},
year = {1983},
}

TY - JOUR
AU - Großmann, Ch.
AU - Kaplan, A. A.
TI - On the rate of convergence of sequential unconstrained minimization techniques
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 1983
PB - Dunod
VL - 17
IS - 3
SP - 267
EP - 292
LA - eng
KW - rate of convergence; sequential unconstrained minimization techniques; SUMT; comparison problems; penalty methods; convergence bounds; quasi- barrier method; parameter selection rules; regularized techniques; methods of centers
UR - http://eudml.org/doc/193418
ER -

References

top
  1. [1] D. P. BERTSEKAS, Onpenalty and multiplier methods for constrained minimization, SIAM J. Control Optimization 14 (1976) 2, 216-235. Zbl0324.49029MR408830
  2. [2] L. BITTNER, Eine Verallgemeinerung des Verfahrens des logarithmischen Potentials von Frisch fur nichtlineare Optimierungsprobleme, Aus : Prékopa, A. (éd.) : Colloque on appl. math, to econ. Budapest, 1965, 43-53. Zbl0142.16905MR189817
  3. [3] I. I. EREMIN, Metod strafov v vypuklom programmirovanii, Dokl. AN SSSR 173 (1967) 4, 748-751. Zbl0155.28405MR214377
  4. [4] A. V. FIACCO, G. P. MCCORMICK, Nonlinear programming : sequential unconstrained minimization techniques, Wiley, New York, 1968 Zbl0193.18805MR243831
  5. [5] E. G. GOL'STEJN, N. V. TRET-JAKOV, Modifieirovannye funkcii Lagranza. Ekon. Mat. Metody 10 (1974) 3, 568-691. 
  6. [6] C. GROBMANN, Rates of convergence in methods of exterior centers, Math. OF Statist. Optimization 9 (1978) 3, 373-388. Zbl0389.65030MR522576
  7. [7] C. GROBMANN, Common properties of nonlinear programming algorithms basing on sequential unconstrained minimizations. Proc. 7-th Sum. School « Nonlin. Anal», 1979. Akademie Verlag, 1981, 107-117. Zbl0468.90065MR639915
  8. [8] C. GROBMANN, Sensitivitatsanalyse als einheitlicher Zugang zu den Verfahren der sukzessiven unrestringierten Minimierung, Diss. B, TU Dresden, 1979. 
  9. [9] C. GROBMANN, A. A. KAPLAN, Strafmethoden und modifizierte Lagrangefunktionen in der nichtlinearen Optimierung, Teubner-Text, Teubner Verlag, Leipzig, 1979. Zbl0425.65035MR581367
  10. [10] C. GROBMANN, G. SCHONTGER, Sensitivitat und Anwendbarkeit von Straf-Barriere- Methoden, ZAMM 57 (1977), 255-264. Zbl0406.90066MR445378
  11. [11] M. HAMALA, A general approach to interior point methods with linear parameter for mathematical programming, TRITA-MAT- 1978-20, Royal Inst. Techn., Stockholm. 
  12. [12] J. HARTUNG, A stable interior penalty method for convex extremal problems, Numer. Math. 29 (1978), 149-158. Zbl0368.90114MR469273
  13. [13] J. HARTUNG, On exponential penalty function methods, Math. OF Statist. Optimization. Zbl0514.90077
  14. [14] A. A. KAPLAN, O skorosti shodimosti metoda strofov, Dokl. AN SSSR 229 (1976) 2, 288-291. Zbl0357.90050
  15. [15] A. A. KAPLAN, K analizu nekotoryh ocenok skorosti shodimosti metoda strafov, Optimizacija 21 (1978). 
  16. [16] A. A. KAPLAN, Methods of nonlinear programming applied to solving variational inequlities, Conf. «Mathematical Programming», Eisenach, 1980. 
  17. [17] B. W. KORT, D. P. BERTSEKAS, Combined primal-dual mathods for convex programming, SIAM J. Control Optimization 14 (1976), 268-294. Zbl0332.90035MR401148
  18. [18] M. KOVAC, O regularizacii nekorrektnyh ekstrema'nyh zadac s ispol'zovaniem metoda ba'ernyh funkcii, Cisl. Analiz. Budapest, 1978, 62-78. 
  19. [19] S. KURCYUSZ, J. MAJCHRZAK, Morrison-type algorithms for constrained optimization. Zbl0443.90093
  20. [20] F. A. LOOTSMA, Boundary properties of penalty functions for constrained minimization, Philips Res.Rept., Suppl. 3, 1970. MR299222
  21. [21] F. A. LOOTSMAConvergence rates of quadratic exterior penalty function methods for solving constrained minimization problems, Philips Res. Rept. 29 (1974), 1-12. Zbl0356.90052MR366036
  22. [22] R. MIFFLIN, Convergence bounds for nonlinear programming algorithms, Math. Programming 8 (1975) 3, 251-271. Zbl0326.90055MR376154
  23. [23] R. MIFFLIN, Rates of convergence for a method of centers algorithm, JOTA 18 (1976) 2, 199-228. Zbl0299.65036MR416600
  24. [24] B. T. POLJAK, O slorosti shodimosti metoda strafnyh funkcij, ZBMMF 11 (1971) 1, 3-11. 
  25. [25] R. T. Rockafellar, Asual approach to solving nonliinear programming problems by unconstrained optimization, Math. Programming 5 (1973), 354-373. Zbl0279.90035MR371416
  26. [26] R. T. ROCKAFELLAR, Augmented Lagrangians and applications of the proximal point algorithm in convex programming, Math. Operations Res. 1 (1976) 2, 97-116. Zbl0402.90076MR418919
  27. [27] V. D. SKARIN, Ob odnoj modifikacii metoda strafnyh funkcij v vypoklom programmirovanii, Trudy Instituta Mat. Meh. Sverdlovsk 5 (1973), 51-62. MR472044
  28. [28] A. N. TIHONOV, F. P. VASIL'EV, Metody resenija nekorreltnyh ekstrema'nyh zadac, Banach Centers Publications, Vol. 3, Warszawa, 1978, 197-342. Zbl0384.65027
  29. [29] F. P. VASIL'EV, O regularizacii nekorrektnyh ekstremal'nyh zadac, Dokl. AN SSSR 241 (1978) 5, 1001-1004. Zbl0423.90059
  30. [30] F. P. VASIL'EV, M. KOVAC, O regularizacii nekorrektnyh ekstremal-nyh zadac v cocetanii so strafnymi finkcijami obscego vida, Problemy Vycisl. Mat. i Sistemnogo Pragrammirovanija, Budapest, 1980, 19-41. Zbl0443.90110MR596240

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.