Generic well-posedness of minimization problems with mixed smooth constraints

In this paper we study mathematical programming problems with mixed smooth constraints in a Banach space and show that most of the problems (in the Baire category sense) are well-posed. Our result is a generalization of a result of A.D. Ioffe et al. [A variational principle for problems with functional constraints, SIAM J. Optim. 12 (2001) 461–478] obtained for finite dimensional Banach spaces. It is also an extension of our recent result [A.J. Zaslavski, Generic well-posedness of minimization problems with mixed continuous constraints, Nonlinear Anal., http://dx.doi.org/10.1016/j.na.2005.10.032] which was obtained for mathematical programming problems with continuous constraints.