On Second Order Sufficient Conditions for Structured Nonlinear Programs in Infinite-Dimensional Function Spaces
J. C. Dunn · 2020
In this expository article, we examine several recently proved second order sufficiency theorems for nonlinear programs with smooth structured nonconvex cost functions and affine constraints in infinite-dimensional function spaces. Sufficient conditions for two nonequivalent species of local optimality are described in this setting, and compared with earlier sufficient conditions for general nonlinear programs in infinite-dimensional normed vector spaces. The structure and smoothness assumptions invoked in the new theorems are satisfied by constrained minimization problems in the calculus of variations and optimal control, and the new sufficient conditions are not far removed from necessary conditions for local optimality.