Error bounds and implicit multifunction theorem in smooth Banach spaces and applications to optimization (Q1878319)

The authors establish local and global error bound estimates for a system of inequalities on a Banach space \(X\) and an implicit theorem for the problem \(S(p):=\{x\in X\mid 0\in F(x,p)\}\) in terms of smooth subdifferentials and presubdifferentials. They also derive a subdifferential calculus, and necessary optimality conditions of Fritz John type for a constrained optimization problem.