Extremal Types for Certain (L sup p) Minimization Problems and Associated Large Scale Nonlinear Programs

摘要

Extremals for constrained minimization problems are classified according to the growth properties of a linear function. Some singular and nonsingular types are investigated; the analysis yields new minimization corollaries of recently developed convergence rate theories for conditional and projected gradient methods and a Newton method for constrained minimization. These results help to explain trends in the behavior of computational procedures for certain large-scale structured nonlinear programs, with particular application to a large class of optimal control problems with linearly constrained inputs. Control problems with bang-bang solutions are considered.