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Summary:
The paper deals with an adaptation of Newton's method for solving nonlinear programming problems. The adaptation is derived by replacing the gradient direction in Rosen's method by Newton's direction and both its convergence and practical aspects are discussed. Convergence properties of another adaptation of Newton's method (suggested by Hájek) are studied, too.
References:
[1] J. Hájek: Minimalisace nákladů při dosažení předepsané přesnosti současně u několika odhadů. Apl. mat., 7 (1962), p. 405-425. MR 0155383
[2] S. Karlin: Mathematical Methods and Theory in Games. Programming and Economics, Vol. I, London 1959. MR 1160778
[3] J. B. Rosen: The Gradient Projection Method for Nonlinear Programming. Part I. Linear Constraints. J. Soc. Industr. Appl. Math., 8 (1960), p. 181 - 217. DOI 10.1137/0108011 | MR 0112750
[4] J. Žáčkova: Dva příspěvky k matematickému programování. Kandidátská disertační práce, matematicko-fyzikální fakulta Karlovy university, Praha 1966.
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