Semistochastic decomposition scheme in mathematical programming and game theory

Tran Quoc Chien

Kybernetika (1991)

  • Volume: 27, Issue: 6, page 535-541
  • ISSN: 0023-5954

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Chien, Tran Quoc. "Semistochastic decomposition scheme in mathematical programming and game theory." Kybernetika 27.6 (1991): 535-541. <http://eudml.org/doc/27450>.

@article{Chien1991,
author = {Chien, Tran Quoc},
journal = {Kybernetika},
keywords = {sup-inf problems; semistochastic decomposition},
language = {eng},
number = {6},
pages = {535-541},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Semistochastic decomposition scheme in mathematical programming and game theory},
url = {http://eudml.org/doc/27450},
volume = {27},
year = {1991},
}

TY - JOUR
AU - Chien, Tran Quoc
TI - Semistochastic decomposition scheme in mathematical programming and game theory
JO - Kybernetika
PY - 1991
PB - Institute of Information Theory and Automation AS CR
VL - 27
IS - 6
SP - 535
EP - 541
LA - eng
KW - sup-inf problems; semistochastic decomposition
UR - http://eudml.org/doc/27450
ER -

References

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  1. G. B. Dantzig, P. Wolfe, The decomposition algorithm for linear programs, Econometrica 29 (1961), 4, 767-778. (1961) Zbl0104.14305MR0138506
  2. J. F. Benders, Partitioning procedures for solving mixed variable programming problems, Numer. Math. 4 (1962), 238-260. (1962) MR0147303
  3. A. Geoffrion, Generalized Benders decomposition, J. Optim. Theory Appl. 10 (1972), 237-260. (1972) Zbl0229.90024MR0327310
  4. T. J. Van Roy, Cross decomposition for mixed integer programming, Mathematical Programming 25 (1983), 46-63. (1983) Zbl0505.90057MR0679253
  5. I. Kornai, T. Liptak, Planning on two levels, In: Application of Mathematics in Economical Research 4, Moscow 1965. In Russian. (1965) MR0214364
  6. R. E. Burkard H. W. Hamacher, J. Tind, On general decomposition schemes in mathematical programming, Mathematical Programming Study 24 (1985), 238-252. (1985) MR0821002
  7. V. Z. Belinskij V. A. Volkonskii S. A. Ivankov A. B. Pomanskii, A. D. Shapiro, Iterative Methods in Game Theory and Mathematical Programming, Nauka, Moscow 1974. In Russian. (1974) 
  8. V. V. Fedorov, Maximin Numerical Methods, Nauka, Moscow 1979. (1979) 
  9. I. Ekeland, R. Temam, Analyse Convexe et Problemes Variationnels, Dunod, Paris 1974. (1974) Zbl0281.49001MR0463993
  10. G. D. Maistrovskii, Gradient methods for finding saddle points, Econom. i Mat. Metody 12 (1976), 917-929. In Russian. (1976) MR0451122
  11. E. G. Golstein, Gradient methods for determination of saddle points and modified Lagrangians, In: Proc. of the Workshop ,,Math. Optimierung - Theorie und Anwendungen'' Wartburg/Eisenach 1983. (1983) 
  12. R. T. Rockafellar, A dual approach to solving nonlinear programming problems by un- constrained optimization, Math. Programming 5 (1973), 354-373. (1973) MR0371416
  13. Tran Quoc Chien, Nondifferentiable and quasidifferentiable duality in vector optimization theory, Kybernetika 21 (1985), 4, 298-321. (1985) Zbl0579.90091MR0815617
  14. Tran Quoc Chien, Fenchel-Lagrange duality in vector fractional programming via abstract duality scheme, Kybernetika 22 (1986), 4, 299-319. (1986) Zbl0616.90081MR0868023
  15. Tran Quoc Chien, Perturbation theory of duality in vector optimization via the abstract duality scheme, Kybernetika 23 (1987), 1, 67-81. (1987) Zbl0615.49007MR0883908
  16. Tran Quoc Chien, Vector nonconvex perturbational duality theory via the abstract duality scheme, Essays on Nonlinear Analysis and Optimization Problems. Ha-Noi 1987. (1987) Zbl0652.90092
  17. B. Gnedenko, The Theory of Probability, Nauka, Moscow 1973. (1973) 
  18. N. N. Vorobiev, Elements of Game Theory: Noncooperative Games, Nauka, Moscow 1984. (1984) 

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