References
J. P.aubin, Applied Functional Analysis. New York 1978.
J. P.Aubin and H.Frankowska, Set-Valued Analysis, Systems and Control: Foundations and Applications, Vol. 2. Boston-Basel-Berlin 1990.
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.
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).
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).
A. Y. Dubovitskii andA. A. Milyutin, Second variations in extremal problems with constraints. Dokl. Akad. Nauk SSSR160, 18–21 (1965).
I. V.Girsanov, Lectures on Mathematical Theory of Extremum Problems. Lecture Notes in Econom. and Math. Systems67, Berlin-Heidelberg-New York 1972.
A. D. Ioffe, On the theory of subdifferential. North-Holland, Amsterdam 1986.
A. D. Ioffe andV. M. Tihomirov, Theory of extremal problems. North-Holland, Amsterdam, 1979.
H. Kawasaki, An envelope like effect of infinitely many inequality constraints on second-order necessary conditions for minimization problems. Math. Programming41, 73–96 (1988).
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).
H. Maurer andJ. Zowe, First and second order necessary and sufficient conditions for infinite dimensional programming problems. Math. Programming16, 98–110 (1979).
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