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Higher-order optimality conditions for a minimax

Published online by Cambridge University Press:  17 April 2009

Do Van Luu  and
W. Oettli
Do Van Luu
Affiliation:
Institute of Mathematics, PO Box 631 BoHo, 10000 Hanoi, Vietnam
W. Oettli
Affiliation:
Fakultät für Mathematik und Informatik, Universität Mannheim, 68131 Mannheim, Germany, e-mail: [email protected]
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Abstract

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Higher-order necessary and sufficient optimality conditions for a nonsmooth minimax problem with infinitely many constraints of inequality type are established under suitable basic assumptions and regularity conditions.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 54 , Issue 3 , December 1996 , pp. 509 - 516
Copyright
Copyright © Australian Mathematical Society 1996

References

[1]Auslender, A., ‘Stability in mathematical programming with nondifferentiable data’, SIAM J. Control Optim. 22 (1984), 239–254.CrossRefGoogle Scholar
[2]Clarke, F.H., Optimization and Nonsmooth Analysis (Wiley, New York, 1983).Google Scholar
[3]Heinecke, G. and Oettli, W., ‘Characterization of weakly efficient points’, Z. Oper. Res. 32 (1988), 375–393.Google Scholar
[4]Ioffe, A.D., ‘Calculus of Dini subdifferentials of functions and contingent coderivatives of set-valued maps’, Nonlinear Anal. 8 (1984), 517–539.CrossRefGoogle Scholar
[5]Ioffe, A.D., ‘Approximate subdifferentials and applications I: The finite dimensional theory’, Trans. Amer. Math. Soc. 281 (1984), 389–416.Google Scholar
[6]Luu, D.V. and Oettli, W., ‘Necessary optimality conditions for nonsmooth minimax problems’, Zeitschrift für Analysis und ihre Anwendungen 12 (1993), 709–721.CrossRefGoogle Scholar
[7]Schwartz, L., Analyse mathématique I (Hermann, Paris, 1967).Google Scholar
[8]Studniarski, M., ‘Necessary and sufficient conditions for isolated local minima of nonsmooth functions’, SIAM J. Control Optim. 24 (1986), 1044–1049.CrossRefGoogle Scholar
[9]Ward, D.E., ‘Directional derivative calculus and optimality conditions in nonsmooth mathematical programming’, J. Inform. Optim. Sci. 10 (1989), 81–96.Google Scholar
[10]Ward, D.E., ‘Exact penalties and sufficient conditions for optimality in nonsmooth optimization’, J. Optim. Theory Appl. 57 (1988), 485–499.CrossRefGoogle Scholar