Invariant Geometric Curvilinear Optimization with Restricted Evolution Dynamics

Abstract

This paper begins with a geometric statement of constraint optimization problems, which include both equality and inequality-type restrictions. The cost to optimize is a curvilinear functional defined by a given differential one-form, while the optimal state to be determined is a differential curve connecting two given points, among all the curves satisfying some given primal feasibility conditions. The resulting outcome is an invariant curvilinear Fritz–John maximum principle. Afterward, this result is approached by means of parametric equations. The classical single-time Pontryagin maximum principle for curvilinear cost functionals is revealed as a consequence.