Remarks on the Newton method for solving nonlinear equality constrained optimization problems

Frank Körner

RAIRO - Operations Research - Recherche Opérationnelle (1990)

  • Volume: 24, Issue: 3, page 287-294
  • ISSN: 0399-0559

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Körner, Frank. "Remarks on the Newton method for solving nonlinear equality constrained optimization problems." RAIRO - Operations Research - Recherche Opérationnelle 24.3 (1990): 287-294. <http://eudml.org/doc/104987>.

@article{Körner1990,
author = {Körner, Frank},
journal = {RAIRO - Operations Research - Recherche Opérationnelle},
keywords = {Kuhn-Tucker point; inverse Hessian; pivoting procedure},
language = {eng},
number = {3},
pages = {287-294},
publisher = {EDP-Sciences},
title = {Remarks on the Newton method for solving nonlinear equality constrained optimization problems},
url = {http://eudml.org/doc/104987},
volume = {24},
year = {1990},
}

TY - JOUR
AU - Körner, Frank
TI - Remarks on the Newton method for solving nonlinear equality constrained optimization problems
JO - RAIRO - Operations Research - Recherche Opérationnelle
PY - 1990
PB - EDP-Sciences
VL - 24
IS - 3
SP - 287
EP - 294
LA - eng
KW - Kuhn-Tucker point; inverse Hessian; pivoting procedure
UR - http://eudml.org/doc/104987
ER -

References

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  1. 1. A. R. CONN and N. I. M. GOULD, On the Location of Indefinite Descent for Nonlinear Programming Algorithm, SIAM J. Num. Anal, 1984, 21 pp. 1162-1179. Zbl0578.65061MR765513
  2. 2. A. L. DONTCHEV and H. Th. JONGEN, On the Regularity of the Kuhn-Tucker Curve, SIAM J. Control Optimization 1986, 24, pp. 169-176. Zbl0598.90086MR826510
  3. 3. R. FLETCHER, Practical Methods of Optimization, John Wïley, Chichester, 1981. Zbl0474.65043MR1867781
  4. 4. S. P. HAN, A Hybrid Method for Nonlinear Programming, Nonlinear Programming 3, Academic Press, New York, 1978, pp. 65-95. Zbl0458.90054MR507859
  5. 5. H. Th. JONGEN, T. MÖBERT and K. TAMMER, On Iterated Minimization in Nonconvex Optimization, Report 488, Twente University of Technology, N. L. Zbl0626.90080
  6. 6. A. KIELBASINSKI and H. SCHWETLICK, Numerische Lineare Algebra, Dt. Verlag d. Wiss., Berlin, 1988. Zbl0635.65024MR1081148
  7. 7. F. KÖRNER and B. LUDERER, A Simultaneous Method for Checking Second-Order Kuhn-Tucker Conditions for Equality Constrained Nonlinear Programming Problems, Syst. Anal. Sim. Mod., 1988, 5, pp. 51-57. Zbl0647.90074MR936145
  8. 8. F. KÖRNER, Remarks on Second-Order Conditions in Connection with the Algorithm of Beale for Quadratic Programming, Europ. J. Oper. Res., 1989, 40, pp. 85-89. Zbl0683.90058MR995553
  9. 9. G. P. McCORMICK, Nonlinear Programming. Theory, Algorithms, and Applications, John Wiley, Chichester, 1983. Zbl0193.18805MR693095
  10. 10. H. SCHWETLICK, Numerische Lösung nichtlinearer Gleichungssysteme, Dt. Verlagd. Wiss., Berlin, 1979. Zbl0408.65027MR519682
  11. 11. A. SHAPIRO, Second-Order Derivatives of Extremal-Value Functions and Optimality Conditions for Semi-Infinite Programs, Math. Oper. Res., 1985,10, pp. 207-219. Zbl0569.90070MR793879
  12. 12. A. SHAPIRO, Second-Order Sensitivity Analysis and Asymptotic Theory of Parametrized Nonlinear Programs, Math. Prog., 1985, 33, pp. 280-299. Zbl0579.90088MR816106
  13. 13. J. E. SPINGARN and R. T. ROCKAFELLAR, The Generic Nature of Optimality Conditions in Nonlinear Programming, Math. Oper. Res., 1979, 40, pp. 425-430. Zbl0423.90071MR549128

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