On Essential Stable Sets of Solutions in Set Optimization Problems

Q. Q. Song (), G. Q. Tang () and L. S. Wang ()
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Q. Q. Song: Guilin University of Technology
G. Q. Tang: Guilin University of Technology
L. S. Wang: China Agricultural University

Journal of Optimization Theory and Applications, 2013, vol. 156, issue 3, No 4, 599 pages

Abstract: Abstract This paper introduces the essential stability for set optimization problems. Some kinds of essential stable sets of weakly minimal and minimal solutions are shown. The graph of minimal solution mappings is not necessarily closed, which is different from weakly minimal solution mappings. The existence of minimum essential sets of minimal solutions is proved.

Keywords: Essential stability; Partial order; Set optimization; Minimal elements; 90C31; 46N10 (search for similar items in EconPapers)
Date: 2013
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DOI: 10.1007/s10957-012-0129-z

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