Abstract
Using the concept of contingent epiderivative, we generalize the notion of subdifferential to a cone-convex set-valued map. Properties of the subdifferential are presented and an optimality condition is discussed.
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References
Jahn, J., Introduction to the Theory of Nonlinear Optimization, Springer, Berlin, Germany, 1996.
Jahn, J., and Rauh, R., Contingent Epiderivatives and Set-Valued Optimization, Mathematical Methods of Operations Research, Vol. 46, pp. 193–211, 1997.
Yang, Q. X., A Hahn-Banach Theorem in Ordered Linear Spaces and Its Applications, Optimization, Vol. 25, pp. 1–9, 1992.
Chen, G. Y., and Jahn, J., Optimality Conditions for Set-Valued Optimization Problems, Mathematical Methods of Operations Research, Vol. 48, 1998.
Jahn, J., Mathematical Vector Optimization in Partially-Ordered Linear Spaces, Peter Lang, Frankfurt, Germany, 1986.
Aubin, J. P., Contingent Derivatives of Set-Valued Maps and Existence of Solutions to Nonlinear Inclusions and Differential Inclusions, Mathematical Analysis and Applications, Part A, Edited by L. Nachbin, Academic Press, New York, New York, pp. 160–229, 1981.
Baier, J., Subdifferentiale für mengenwertige Abbildungen, Diplom Thesis, University of Erlangen-Nürnberg, 1997.
Zowe, J., Konvexe Funktionen und konvexe Dualitätstheorie in geordneten Vektorräumen, Habilitation Thesis, University of Würzburg, 1976.
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Baier, J., Jahn, J. On Subdifferentials of Set-Valued Maps. Journal of Optimization Theory and Applications 100, 233–240 (1999). https://doi.org/10.1023/A:1021733402240
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DOI: https://doi.org/10.1023/A:1021733402240