Journal
MATHEMATICS
Volume 10, Issue 3, Pages -Publisher
MDPI
DOI: 10.3390/math10030316
Keywords
K-preinvex multi-valued map; normal subdifferential; equilibrium-like function; set-valued vector optimization problem; super efficient solutions
Categories
Funding
- Shanghai Leading Talents Program of the Shanghai Municipal Human Resources and Social Security Bureau [20LJ2006100]
- Innovation Program of Shanghai Municipal Education Commission [15ZZ068]
- Program for Outstanding Academic Leaders in Shanghai City [15XD1503100]
- Grant MOST [106-2923-E-039-001-MY3]
- MOST project in Taiwan [MOST 110 2410 H 037 001]
- KMU joint R and D Project [NKUST KMU 110KK002]
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This paper investigates the properties of K-preinvex set-valued maps using the normal subdifferential and equilibrium-like function. It establishes sufficient conditions for the existence of super minimal points of a K-preinvex set-valued map and provides necessary optimality terms for a general type of super efficiency.
In this paper, by using the normal subdifferential and equilibrium-like function we first obtain some properties for K-preinvex set-valued maps. Secondly, in terms of this equilibrium-like function, we establish some sufficient conditions for the existence of super minimal points of a K-preinvex set-valued map, that is, super efficient solutions of a set-valued vector optimization problem, and also attain necessity optimality terms for a general type of super efficiency.
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