Conjugate Maps, Subgradients and Conjugate Duality in Set-Valued Optimization

Abstract

Using the concept of supremum/infimum of a set, defined in terms of the closure of the set, we introduce the notions of conjugate and biconjugate maps as well as that of subgradients of a set-valued map. Conjugate duality results are also established for a set-valued optimization problem.

Keywords:

• Conjugate map
• Duality
• Set-valued optimization
• Subgradients
• Supremum

AMS Subject Classification:

• 90C46
• 54C60

ACKNOWLEDGMENT

The author is thankful for the grant provided by CSIR to support this research.