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

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

MathSciNet review:
0351080

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References | Similar Articles | Additional Information

**1.**H. A. Antosiewicz,*Newton's method for boundary value problems*, J. Comput. System Sci. 2 (1968), 177-202. MR 39 #5055. MR**243734****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), 115-124. MR**324406****4.**J. M. Ortega and W. C. Rheinboldt,*Iterative solutions of nonlinear equations in several variables*, Academic Press, New York, 1970. MR 42 #8686. MR**273810****5.**L. B. Rall,*Computational solution of nonlinear operator equations*, Wiley, New York, 1969. MR 39 #2289. MR**240944****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.**R. A. Tapia,*An application of a Newton-like method to the Euler-Lagrange equation*, Pacific J. Math. 29 (1969), 235-246. MR 40 #3713. MR**250479****9.**R. A. Tapia,*The weak Newton method and boundary value problems*, SIAM J. Numer. Anal. 6 (1969), 539-550. MR 41 #9439. MR**264848****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