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Constrained optimization problems

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Learning Automata and Stochastic Optimization

Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 225))

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References

  1. Clarke F H, Dem'yanov V F, Gianessi F 1989 Nonsmooth Optimization and Related Topics. Plenum Press, New York

    Google Scholar 

  2. Najim K 1989 Process Modeling and Control in Chemical Engineering. Marcel Dekker, New York

    Google Scholar 

  3. Najim K, Oppenheim G 1991 Learning systems: theory and applications. IEE Proceedings Computer and Digital Techniques 138:183–192

    Google Scholar 

  4. Najim K, Poznyak A S 1994 Learning Automata: Theory and Applications. Pergamon Press, Oxford

    Google Scholar 

  5. Wong E 1973 Recent progress in stochastic processes — a survey”, IEEE Trans. on Information Theory. 19:262–275

    Google Scholar 

  6. Bertsekas D P 1982 Constrained Optimization and Lagrange Multiplier Methods. Academic Press, New York

    Google Scholar 

  7. Rockafellar R T 1993 Lagrange multipliers and optimality. SIAM Review 35:183–238

    Google Scholar 

  8. Rockafellar R T 1970 Convex Analysis. Princeton University Press, Princeton

    Google Scholar 

  9. Sposito V A 1975 Linear and Nonlinear Programming. The Iowa State University Press/AMES

    Google Scholar 

  10. Martos B 1975 Nonlinear Programming Theory and Methods. North-Holland Publishing Company, Amsterdam

    Google Scholar 

  11. Whittle P 1971 Optimization under Constraints. Wiley-Interscience, New York

    Google Scholar 

  12. D.G. Luenberger D G 1965 Introduction to Linear and Nonlinear Programming. Addison-Wesley, London

    Google Scholar 

  13. Avriel M 1976 Nonlinear Programming: Analysis and Methods. Prentice-Hall, Englewood Cliffs

    Google Scholar 

  14. Liukkonen J R, Levine A 1994 On convergence of iterated random maps. SIAM J. Control and Optimization 32:1752–1762

    Google Scholar 

  15. Bush R R, Mosteller F 1958 Stochastic Models for Learning. John Wiley & Sons, New York

    Google Scholar 

  16. Narendra K S, Thathachar M A L 1989 Learning Automata an Introduction. Prentice-Hall, Englewood Cliffs

    Google Scholar 

  17. Najim K, Poznyak A S 1996 Multimodal searching technique based on learning automata with continuous input and changing number of actions. IEEE Trans. on Systems, Man, and Cybernetics 26:666–673

    Google Scholar 

  18. Poznyak A S 1973 Learning automata in stochastic programming problems. Automation and Remote Control 34:1608–1619

    Google Scholar 

  19. Baba N 1984 New Topics in Learning Automata Theory and Applications. Springer-Verlag, Berlin

    Google Scholar 

  20. Polyak B T 1987 Introduction to Optimization. Optimization Software, Publication Division, New York

    Google Scholar 

  21. Kaplinskii A I, Propoi A I 1970 Stochastic approach to nonlinear programming problems. Automation and Remote Control 31:448–459

    Google Scholar 

  22. Kaplinskii A I, Poznyak A S, Propoi A I 1971 Optimality conditions for certain stochastic programming problems. Automation and Remote Control 32:1210–1218

    Google Scholar 

  23. Kaplinskii A I, Poznyak A S, Propoi A I 1971 Some methods for the solution of stochastic programming problems. Automation and Remote Control 32:1609–1616

    Google Scholar 

  24. Nazin A V, Poznyak A S 1986 Adaptive Choice of Variants. (in Russian) Nauka, Moscow

    Google Scholar 

  25. Vajda S 1972 Probabilistic Programming. Academic Press, New York

    Google Scholar 

  26. Zangwill W I 1969 Nonlinear Programming: A Unified Approach. Prentice-Hall, Englewood Cliffs

    Google Scholar 

  27. Garcia C B, Zangwill W I 1981 Pathways to Solutions, Fixed Points, and Equilibria. Prentice-Hall, Englewood Cliffs

    Google Scholar 

  28. Doob J L 1953 Stochastic Processes. John Wiley & Sons, New York

    Google Scholar 

  29. Charnes A, Cooper W W, Thompson G J 1964 Critical path analysis via chance constrained and stochastic programming. Operations Res. 12:460–470

    Google Scholar 

  30. Ash R B 1972 Real Analysis and Probability. Academic Press, New York

    Google Scholar 

  31. Arrow K J, Hurwics L, Uzawa H 1961 Constraint qualifications and maximization problems. Naval Res. Log. Quart. 8:175–191

    Google Scholar 

  32. Robbins H, Siegmund D 1971 A convergence theorem for nonnegative almost supermartingales and some applications. In: Rustagi J S (ed) 1971 Optimizing Methods in Statistics. Academic Press, New York

    Google Scholar 

  33. Albert A 1972 Regression and the Moore-Penrose Pseudoinverse. Academic Press, New York

    Google Scholar 

  34. Slater M 1950 Lagrange multipliers revisted: a contribution to nonlinear programming. Cowles Discussion Paper 403

    Google Scholar 

  35. Spingarn J E, Rockafellar R T 1979 The generic nature of optimal conditions in nonlinear programs. Mathematics of Operation Research 4:425–430

    Google Scholar 

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© 1997 Springer-Verlag London Limited

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(1997). Constrained optimization problems. In: Learning Automata and Stochastic Optimization. Lecture Notes in Control and Information Sciences, vol 225. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0015107

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  • DOI: https://doi.org/10.1007/BFb0015107

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-76154-9

  • Online ISBN: 978-3-540-40938-0

  • eBook Packages: Springer Book Archive

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