Primal and dual formulations of sequential gradientrestoration algorithms for trajectory optimization problems
Abstract
One of the most effective firstorder algorithms for solving trajectory optimization problems is the sequential gradientrestoration algorithm (SGRA). Originally developed in the primal formulation (PSGRA), this algorithm is extended to incorporate a dual formulation (DSGRA). Both the primal formulation and the dual formulation involve a sequence of twophase cycles, each cycle including a gradient phase and a restoration phase. In turn, each iteration of the gradient phase and the restoration phase requires the solution of an auxiliary minimization problem (AMP). In the primal formulation, the AMP is solved with respect to the variations of the state, the control and the parameter. In the dual formulation, the AMP is solved with respect to the Lagrange multipliers. A characteristic of the dual formulation is that the AMP's associated with the gradient phase and the restoration phase of SGRA can be reduced to mathematical programming problems involving a finite number of parameters as unknowns. A comparison of the primal formulation and the dual formulation is presented. The comparison is done in terms of several trajectory optimization problems having current aerospace interest.
 Publication:

Acta Astronautica
 Pub Date:
 August 1986
 DOI:
 10.1016/00945765(86)900287
 Bibcode:
 1986AcAau..13..491M
 Keywords:

 Algorithms;
 Optimal Control;
 Sequential Analysis;
 Trajectory Optimization;
 Transfer Orbits;
 Wind Shear;
 Aeroassist;
 Iteration;
 Lagrange Multipliers;
 Astrodynamics