Volume 7, Number 1, April 2006, pp. 1937  
Andreas Hamel and Andreas Löhne  
Key words:  
set relations, setvalued variational principle, minimal point theorem, setvalued optimization  
Mathematices Subject Classification: 58E30, 46N10  


Abstract:  
We present two existence principles for minimal points of subsets of the product space X × 2^{Y}, where X stands for a separated uniform space and Y a topological vector space. The two principles are distinct with respect to the involved ordering structure in 2^{Y}.
We derive from them new variants of Ekeland's principle for setvalued maps as well as a minimal point theorem in X × Y and Ekeland's principle for vectorvalued functions. 

Minimal element theorems and Ekeland's principle with set relations  