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General necessary and sufficient conditions for constrained optimum problems

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References

  1. J. P.aubin, Applied Functional Analysis. New York 1978.

  2. J. P.Aubin and H.Frankowska, Set-Valued Analysis, Systems and Control: Foundations and Applications, Vol. 2. Boston-Basel-Berlin 1990.

  3. A.Ben-Tal, Second order theory of extremum problems. In: Extremal methods and systems analysis, A. V. Fiacco and K. Kortanek, eds., 336–356, Berlin-Heidelberg-New York 1980.

  4. A. Ben-Tal andJ. Zowe, A unified theory of first and second order conditions for extremum problems in topological vector spaces. Math. Programming Stud.19, 39–76 (1982).

    Google Scholar 

  5. A. Y. Dubovitskii andA. A. Milyutin, Extremum problems with constraints. Dokl. Akad. Nauk SSSR,149, 759–762 (1963)=Soviet Math. Dokl.4, 452–455 (1963).

    Google Scholar 

  6. A. Y. Dubovitskii andA. A. Milyutin, Second variations in extremal problems with constraints. Dokl. Akad. Nauk SSSR160, 18–21 (1965).

    Google Scholar 

  7. I. V.Girsanov, Lectures on Mathematical Theory of Extremum Problems. Lecture Notes in Econom. and Math. Systems67, Berlin-Heidelberg-New York 1972.

  8. A. D. Ioffe, On the theory of subdifferential. North-Holland, Amsterdam 1986.

    Google Scholar 

  9. A. D. Ioffe andV. M. Tihomirov, Theory of extremal problems. North-Holland, Amsterdam, 1979.

    Google Scholar 

  10. H. Kawasaki, An envelope like effect of infinitely many inequality constraints on second-order necessary conditions for minimization problems. Math. Programming41, 73–96 (1988).

    Google Scholar 

  11. E. S. Levitin, A. A. Milyutin andN. P. Osmolovskii, Higher order conditions for a local minimum in problems with constraints. Uspehi Mat. Nauk33, 85–148 (1978).

    Google Scholar 

  12. H. Maurer andJ. Zowe, First and second order necessary and sufficient conditions for infinite dimensional programming problems. Math. Programming16, 98–110 (1979).

    Google Scholar 

  13. Z.Páles and V. M.Zeidan, Nonsmooth optimum problems with constraints. SIAM J. Control Optim., to appear.

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Dedicated to Professor Heinz König on the occasion of his 65th birthday

The research was performed when the author received a Research Fellowship of the Humboldt Foundation in Saarbrücken. The support of the Humboldt Foundation is gratefully acknowledged.

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Páles, Z. General necessary and sufficient conditions for constrained optimum problems. Arch. Math 63, 238–250 (1994). https://doi.org/10.1007/BF01189826

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  • DOI: https://doi.org/10.1007/BF01189826

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