Abstract
In this paper, we establish a theorem of the alternative in ordered linear topological spaces. Then, optimality conditions for the optimization of set-valued maps are obtained.
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References
Borwein, J., Multivalued Convexity and Optimization: A Unified Approach to Inequality and Equality Constraints, Mathematical Programming, Vol. 13, pp. 183–199, 1977.
Giannessi, F., Theorems of the Alternative for Multifunctions with Applications to Optimization: General Results, Journal of Optimization Theory and Applications, Vol. 55, pp. 233–256, 1987.
Ferrero, O., Theorems of the Alternative for Set-Valued Functions in Infinite-Dimensional Spaces, Optimization, Vol. 20, pp. 167–175, 1989.
Tiel, J. V., Convex Analysis: An Introductory Text, John Wiley and Sons, New York, New York, 1984.
Corley, H. W., Optimality Conditions for Maximization of Set-Valued Functions, Journal of Optimization Theory and Applications, Vol. 58, pp. 1–10, 1988.
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Li, Z. A Theorem of the Alternative and Its Application to the Optimization of Set-Valued Maps. Journal of Optimization Theory and Applications 100, 365–375 (1999). https://doi.org/10.1023/A:1021786303883
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DOI: https://doi.org/10.1023/A:1021786303883