Bonnans, Joseph Frédéric On an algorithm for optimal control using Pontryagin’s maximum principle. (English) Zbl 0592.49018 SIAM J. Control Optimization 24, 579-588 (1986). The author studies the well-posedness and the convergence of an iterative algorithm proposed by Y. Sakawa and Y. Shindo [IEEE Trans. Autom. Control AC-25, 1149-1153 (1980; Zbl 0489.49017)] for the resolution of an optimal control problem associated with an ordinary differential equation. It is shown that in the case where the control enters in a linear way in the state equation and in a quadratic way in the criterion, the algorithm is equivalent to a gradient plus projection method in some new metric. Reviewer: O.Cârjă Cited in 11 Documents MSC: 49M05 Numerical methods based on necessary conditions 49K15 Optimality conditions for problems involving ordinary differential equations 65K10 Numerical optimization and variational techniques 90C52 Methods of reduced gradient type 93B40 Computational methods in systems theory (MSC2010) 93C10 Nonlinear systems in control theory 93C15 Control/observation systems governed by ordinary differential equations Keywords:well-posedness; convergence; iterative algorithm; gradient plus projection method Citations:Zbl 0489.49017 PDFBibTeX XMLCite \textit{J. F. Bonnans}, SIAM J. Control Optim. 24, 579--588 (1986; Zbl 0592.49018) Full Text: DOI Link