Some existence results of efficiency in vector optimization

X. X. Huang and X. M. Yang

Mathematical Methods of Operations Research, 2001, vol. 53, issue 3, 401 pages

Abstract: In this paper, we present several existence results for efficient solutions and efficient points in vector optimization problems. Firstly, we apply a corollary of a recently obtained Caristi-Kirk fixed point theorem ([3]) to obtain existence results for efficient solutions of a vector optimization problem, which generalize the existence theorems of efficient solutions in [2] (Theorem 9 and its Corollary). Secondly, we generalize Theorem 10 in [2] to the vector case, obtaining an existence result for efficient points of a vector optimization problem. As a result, an open problem following the Corollary of Theorem 10 in [2] is solved in some way. Finally, the concept of nuclear cones introduced in [5] is extended, somehow answering another open question in [2] (in the Remark following the Corollary of Theorem 9). Applying this concept of generalized nuclear cones, we derive another existence theorem of efficient points. Copyright Springer-Verlag Berlin Heidelberg 2001

Keywords: Key words: Caristi-Kirk fixed point theorem; vector variational principle; efficiency; nuclear cone (search for similar items in EconPapers)
Date: 2001
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DOI: 10.1007/s001860100118

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