This is a preview of subscription content, log in via an institution to check access.
References
P.T. Boggs and J.E. Dennis, Jr., “An analysis of the discretized analog of steepest descent”, to appear.
A. Cauchy, “Methode générale pour la résolution des systems d'equations simultanes”,Comptes Rendus Ilebdomadaires des Séances de l'Academic des Sciences 25 (1847) 536–538.
D.F. Cudia, “The geometry of Banach spaces: Smoothness”,Transactions of the American Mathematical Society 110 (1964) 284–314.
H.B. Curry, “The method of steepest descent for nonlinear minimization problems”,The Quarterly Journal of Mechanics and Applied Mathematics 2 (1944) 258–261.
J.W. Daniel,“The approximate minimization of funetionals” (Prentice-Hall, Englewood Cliffs, N.J., 1971).
A.A. Goldstein, “Convex programming in Hilbert space”,Bulletin of the American Mathematical Society 70 (1964) 709–710.
A.A. Goldstein, “Constructive real analysis” (Harper and Row, New York, 1967).
M. Golomb, “Zur theorie der nichlinear Integral-gleichungen, Integral-gleichungssystem und allgemeinen Functional-gleichungen”,Mathematische Zeitschrift 39 (1934) 45–75.
M. Golomb and R.A. Tapia, “The metric gradient in normed linear spaces”,Numerische Mathematik 20 (1972) 115–124.
L.V. Kantorovich, “On an effective method of solution of extremal problems for a quadratic functional”,Doklady Akademii Nauk SSSR 4 (1945) 531–538.
L.V. Kantorovich and G.P. Akilov, “Functional analysis in normed spaces” (Pergamon, New York, 1964).
D.G. Luenberger, “Introduction to linear and nonlinear programming” (Addison-Wesley, Reading, Mass., 1973).
G.P. McCormick, and R.A. Tapia, “The gradient projection method under mild differentiability conditions”,SIAMJournal on Control 10 (1972) 93–98.
J.M. Ortega and W.C. Rheinboldt, “Iterative solution of nonlinear equations in several variables” (Academic Press, New York, 1970).
R.V. Southwell, “Stress calculations in frameworks by the method of systematic relaxation of constraints”,Proceedings of the Royal Society 151 (1935) 56–95.
R.A. Tapia, “A characterization of inner product spaces”,Proceedings of the American Mathematical Society 41 (1973) 569–574.
P. Wolfe, “Convergence conditions for ascent methods”,SIAM Review 11 (1969) 226–234.
P. Wolfe, “Convergence conditions for ascent methods II: Some corrections”,SIAM Review 13 (1971) 185–188.
W.I. Zangwill, “Nonlinear programming: a unified approach” (Prentice-Hall, Englewood Cliffs, N.J., 1969).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Byrd, R.H., Tapia, R.A. An extension of Curry's theorem to steepest descent in normed linear spaces. Mathematical Programming 9, 247–254 (1975). https://doi.org/10.1007/BF01681347
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01681347