An algebraic criterion for strong stability of stationary solutions of nonlinear programs with a finite number of equality constraints and an abstract convex constraint

This paper addresses strong stability, in the sense of Kojima, of stationary solutions of nonlinear programs Pro with a finite number of equality constraints and one abstract convex constraint defined by the closed convex set K. It intends to extend results of our former paper that treated nonlinear programs Pro in a special case that K is the set of nonnegative symmetric matrices S+. Firstly, it deduces properties of eigenvalues of the Euclidean projector on K. Secondly, it extends the results to programs Pro in case that the convex set K satisfies the regular boundary condition that S+ always satisfies.