2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/71987We obtain a generalization of Noether's invariance principle for optimal control problems with equality and inequality state-input constraints. The result relates the invariance properties of the problems with the existence of conserved quantities along the constrained Pontryagin extremals. A result of this kind was posed as an open question by Vladimir Tikhomirov, in 1986.To be presented at the 6th WSEAS International Conference on Applied Mathematics, Corfu, Greece, August 17-19, 2004. Accepted for publication in the journal WSEAS Transactions on MathematicsOptimization and Control49K15text