Benson Proper Efficiency in the Vector Optimization of Set-Valued Maps

Z. F. Li
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Z. F. Li: University of Inner Mongolia

Journal of Optimization Theory and Applications, 1998, vol. 98, issue 3, No 6, 623-649

Abstract: Abstract This paper extends the concept of cone subconvexlikeness of single-valued maps to set-valued maps and presents several equivalent characterizations and an alternative theorem for cone-subconvexlike set-valued maps. The concept and results are then applied to study the Benson proper efficiency for a vector optimization problem with set-valued maps in topological vector spaces. Two scalarization theorems and two Lagrange multiplier theorems are established. After introducing the new concept of proper saddle point for an appropriate set-valued Lagrange map, we use it to characterize the Benson proper efficiency. Lagrange duality theorems are also obtained

Keywords: Set-valued maps; vector optimization; Benson proper efficiency; cone subconvexlikeness; proper saddle points (search for similar items in EconPapers)
Date: 1998
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Citations: View citations in EconPapers (14)

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DOI: 10.1023/A:1022676013609

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