The Pontryagin and Euler-Lagrange necessary conditions (Q1322299)

The author considers an optimal control problem with differential inclusion. It has been shown in other works that different sets of necessary conditions can be obtained. The benefit is that a nonminimizing arc may satisfy one set of necessary conditions and fails to satisfy the conditions for another set of necessary conditions. Thus, it will be of interest and great value to see if an adjoint arc and multipliers can be found that satisfy different sets of necessary conditions simultaneously. The author's work is toward this objective. He proves that there is an adjoint arc that satisfies Pontryagin and Euler/Lagrange necessary conditions.