Abstract

The purpose of this paper is to establish a Fritz John type first order necessary condition for constrained nonlinear optimization problems in infinite dimensional spaces via the finite codimension condition. Different form the known constraint qualifications in infinite dimensional optimization theory, the finite codimension condition introduced in this paper is much easy to be verified. To illustrate this, some equivalent verification conditions for finite codimension condition are proposed. As applications, the first order necessary conditions for optimal control problems governed by various control systems are derived in a uniform way.