Abstract.
Generalized properly efficient solutions of a vector optimization problem (VP) are defined in terms of various tangent cones and a generalized directional derivative. We study their basic properties and relationships and show that under certain conditions, a generalized properly efficient solution of (VP), defined by the adjacent cone, is a generalized Kuhn-Tucker properly efficient solution of (VP). Furthermore, using subgradients defined by closed convex tangent cones, we give a necessary optimality condition for a generalized properly efficient solution of (VP) defined by the adjacent cone.
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Manuscript received: March 2000/Final version received: October 2000
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Ward, D., Lee, G. Generalized properly efficient solutions of vector optimization problems. Mathematical Methods of OR 53, 215–232 (2001). https://doi.org/10.1007/s001860100112
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DOI: https://doi.org/10.1007/s001860100112