From the book of bertesekas(1999),borwein(2006), we learned some constraint qualifications on R^n spaces,such as:

Linear independence constraint qualification(1951) Mangasarian–Fromovitz constraint qualification(1967) , Constant rank constraint qualification , Constant positive linear dependence constraint qualification , Quasi-normality constraint qualification

when it is in Infinite-dimensional optimization, Question: How to get constraint qualifications conditions for optimization on banach spaces