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3.1 Literature
This chapter is based on the report H.F. Ravn: Upper Boundary Methods. IMSOR, Research Report No. 10, 1980, see also
R.V.V. Vidal: Notes in Static and Dynamic Optimization. IMSOR, 1981.
The early (incorrect) derivation of the Linear Discrete Maximum Principle is in S. Katz: Best Operating points for staged systems. Ind. & Eng. Chem. Fundamentals, Vol. 1, No. 4, 1962, pp. 226–240.
L.T. Fan, Ch. S. Wang: The Discrete Maximum Principle. Wiley, 1964, and the discussion around it
F. Horn, R. Jackson: Discrete Maximum Principle. Ind. & Eng. Chem. Fundamentals, Vol. 4, No. 1, pp. 110–112, No. 4, pp. 487–488, 1965.
R. Jackson, F. Horn: On Discrete Analogues of Pontryagin's Maximum Principle. Int. J. Control, Vol. 1, No. 4, 1965, pp. 389–395.
M.M. Denn: Discrete Maximum Principle. Ind. & Eng. Chem. Fundamentals, Vol. 4, No. 2, 1965, pp. 240.
The correct derivation of the Linear Discrete Maximum Principle with convexity assumption is in H. Halkin: Optimal Control for Systems Described by Difference Equations. In: C.T. Leonder (ed.): Advances in Control Systems, Vol. I. Academic Press, 1964.
H. Halkin: A Maximum Principle of the Pontryagin Type for Systems Described by Nonlinear Difference Equations. SIAM J. Control, Vol. 4, No. 1, 1966, pp. 90–111.
A.I. Propoi: The Maximum Principle for Discrete Control Systems. Automation and Remote Control, Vol. 26, No. 7, 1965, pp. 1167–1177, and with directional convexity
J.M. Holtzman: Convexity and the Maximum Principle for Discrete Systems. IEEE Trans. Autom. Control, Vol. AC-11, No. 1, 1966, pp. 30–35.
J.M. Holtzman: On the Maximum Principle for Nonlinear Discrete-Time Systems. IEEE Trans Autom. Control, Vol. AC-11, No. 2, 1966, pp. 273–274.
J.M. Holtzman, H. Halkin: Directional Convexity and the Maximum Principle for Discrete Systems. SIAM J. Control, Vol. 4, No. 2, 1966, pp. 263–275.
M.D. Canon, C.D. Cullum Jr., E. Polak: Theory of Optimal Control and Mathematical Programming. McGraw-Hill, 1970.
Numerical algorithms under assumptions of the existence of a linear support are discussed in S. Katz: Best Operating Points for Staged Systems. Ind. & Eng. Chem. Fundamentals, Vol. 1, No. 4, 1962, pp. 226–240.
M.M. Denn, R. Aris: Green's Functions and Optimal Systems. I, II, III. Ind. & Eng. Chem. Fundamentals, Vol. 4, No. 1, pp. 7–16, No. 2, pp. 213–222, No. 3, pp. 248–257, 1965.
M.M. Denn: Convergence of a Method of Successive Approximations in the Theory of Optimal Processes. Ind. & Eng. Chem. Fundamentals, Vol. 4, p. 231, 1965.
L.T. Fan, C.S. Wang: The Discrete Maximum Principle. Wiley, 1964.
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(1983). Multistage systems. In: Nahorski, Z., Ravn, H.F., Vidal, R.V.V. (eds) Optimization of Discrete Time Systems. Lecture Notes in Control and Information Sciences, vol 51. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0044341
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