LEGENDRE CONDITIONS FOR A VARIATIONAL PROBLEM WITH ONE-SIDED PHASE CONSTRAINTS
Hidefumi Kawasaki, Sayuri Koga · Journal of the Operations Research Society of Japan · 1995
This paper is concerned with a variational problem with inequality phase constraints. We present second-order necessary conditions (Legendre condition) for weak minimal solutions of the variational problem. Our optimality conditions give an information about the Hessian of the integrand at not only inactive points but also active points. Since the present constraints do not include x, our conditions differ from the Legendre-Clebsch condition.