Sequential conjugate gradient-restoration algorithm for optimal control problems with nondifferential constraints, † Part I

Abstract

Abstract A sequential conjugate gradient-restoration algorithm is developed in order to solve optimal control problems involving a functional subject to differential constraints, nondifferential constraints, and terminal constraints. The algorithm is composed of a sequence of cycles, each cycle consisting of two phases, a conjugate gradient phase and a restoration phase. The conjugate gradient phase involves a single iteration and is designed to decrease the value of the functional, while satisfying the constraints to first order. During this iteration, the first variation of the functional is minimized, subject to the linearized constraints. The minimization is performed over the class of variations of the control and the parameter which are equidistant from some constant multiple of the corresponding variations of the previous conjugate gradient phase. For the special case of a quadratic functional subject to linear constraints, various orthogonality and conjugacy conditions hold. The restoration phase ...