17- https://doi.org/10.1080/0233193031000120051
Weak Subdifferential of Set-Valued Mappings
- Jun 1, 2003
- Optimization
- Wen Song
In this note we introduce a notion of the weak contingent generalized gradient for set-valued mappings associated with the contingent epiderivative of set-valued mappings introduced in "E. Bednarczuk and W. Song (1998). Contingent epiderivative and its applications to set-valued optimization. Control and Cybernetics, 27, 376-386; G.Y. Chen and J. Jahn (1998). Optimally conditions for set-valued optimization problems. Mathematical Methods of Operations Research, 48, 187-200." and prove that, under some additional condition, it coincides with the weak subdifferential introduced in "T. Tanino (1992). Conjugate duality in vector optimization. Journal of Mathematical Analysis and Applications, 167, 84-97." when the set-valued map is cone-convex. We also study the weak contingent generalized gradient of a sum of two set-valued mappings and optimality conditions for a set-valued vector optimization problem.
- # Set-valued Optimization
- # Mathematical Methods Of Operations Research
- # Set-valued Mappings
- # Duality In Vector Optimization
- # Set-valued Optimization Problem
- # Contingent Epiderivative
- # Weak Subdifferential
- # Conjugate Duality
- # Vector Optimization
- # Additional Condition
