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Near-Subconvexlikeness in Vector Optimization with Set-Valued Functions

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Abstract

A new class of generalized convex set-valued functions, termed nearly-subconvexlike functions, is introduced. This class is a generalization of cone-subconvexlike maps, nearly-convexlike set-valued functions, and preinvex set-valued functions. Properties for the nearly-subconvexlike functions are derived and a theorem of the alternative is proved. A Lagrangian multiplier theorem is established and two scalarization theorems are obtained for vector optimization.

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Authors
  1. X. M. Yang
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  2. D. Li
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  3. S. Y. Wang
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Yang, X.M., Li, D. & Wang, S.Y. Near-Subconvexlikeness in Vector Optimization with Set-Valued Functions. Journal of Optimization Theory and Applications 110, 413–427 (2001). https://doi.org/10.1023/A:1017535631418

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  • DOI: https://doi.org/10.1023/A:1017535631418

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