A general approach to Newton's method for Banach space problems with equality constraints

Author:
R. A. Tapia

Journal:
Bull. Amer. Math. Soc. **80** (1974), 355-360

MSC (1970):
Primary 47H15, 49D15, 65J05

MathSciNet review:
0351080

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References | Similar Articles | Additional Information

**1.**H. A. Antosiewicz,*Newton’s method and boundary value problems*, J. Comput. System Sci.**2**(1968), 177–202. MR**0243734****2.**J. E. Dennis, Jr.,*Variations on Newton's method*, Doctoral thesis, University of Utah, Salt Lake City, Ut., 1966.**3.**M. Golomb and R. A. Tapia,*The metric gradient in normed linear spaces*, Numer. Math.**20**(1972/73), 115–124. MR**0324406****4.**J. M. Ortega and W. C. Rheinboldt,*Iterative solution of nonlinear equations in several variables*, Academic Press, New York-London, 1970. MR**0273810****5.**Louis B. Rall,*Computational solution of nonlinear operator equations*, With an appendix by Ramon E. Moore, John Wiley & Sons, Inc., New York-London-Sydney, 1969. MR**0240944****6.**S. M. Robinson,*Extension of Newton's method to mixed systems of nonlinear equations and inequalities*, Rep. 1161, Mathematics Research Center, University of Wisconsin, Madison, Wise, 1971.**7.**M. Stein,*On methods of obtaining solutions of fixed end point problems in the calculus of variations*, Doctoral thesis, University of California, Los Angeles, Calif., 1950.**8.**Richard A. Tapia,*An application of a Newton-like method to the Euler-Lagrange equation.*, Pacific J. Math.**29**(1969), 235–246. MR**0250479****9.**Richard A. Tapia,*The weak Newton method and boundary value problems*, SIAM J. Numer. Anal.**6**(1969), 539–550. MR**0264848****10.**R. A. Tapia,*Newton's method for problems with equality constraints*, SIAM J. Numer. Anal. (to appear).**11.**R. A. Tapia,*Newton's method for optimization problems with equality constraints*, SIAM J. Numer. Anal. (to appear).

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DOI:
https://doi.org/10.1090/S0002-9904-1974-13503-2