Constraint Qualification with Schauder Basis for Infinite Programming Problems

We consider infinite programming problems with constraint sets defined by systems of infinite number of inequalities and equations given by continuously differentiable functions defined on Banach spaces. In the approach proposed here we represent these systems with the help of coefficients in a given Schauder basis. We prove Abadie constraint qualification under the new infinite-dimensional Relaxed Constant Rank Constraint Qualification Plus and we discuss the existence of Lagrange multipliers via Hurwicz set. The main tools are: Rank Theorem and Lyusternik–Graves theorem.