Regularity and Conjugacy for Constrained Variational Problems
Javier F. Rosenblueth · WSEAS TRANSACTIONS on SYSTEMS archive · 2020
For problems in the calculus of variations involving equality and inequality mixed constraints we characterize, in terms of an extended notion of conjugate points, the sign of a quadratic form which corresponds to the second variation of the integral to be minimized. Second order necessary conditions are then derived assuming the well-known constraint qualification of regularity in the sense that, with respect to the set of mixed constraints, both the tangent cone and the set of tangential constraints coincide.