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), 355360
MSC (1970):
Primary 47H15, 49D15, 65J05
MathSciNet review:
0351080
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References 
Similar Articles 
Additional Information
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H.
A. Antosiewicz, Newton’s method and boundary value
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177–202. MR 0243734
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J. E. Dennis, Jr., Variations on Newton's method, Doctoral thesis, University of Utah, Salt Lake City, Ut., 1966.
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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.
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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.
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Richard
A. Tapia, An application of a Newtonlike method to the
EulerLagrange equation., Pacific J. Math. 29 (1969),
235–246. MR 0250479
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 9.
Richard
A. Tapia, The weak Newton method and boundary value problems,
SIAM J. Numer. Anal. 6 (1969), 539–550. MR 0264848
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 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).
 1.
 H. A. Antosiewicz, Newton's method for boundary value problems, J. Comput. System Sci. 2 (1968), 177202. 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), 115124. 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 Newtonlike method to the EulerLagrange equation, Pacific J. Math. 29 (1969), 235246. MR 40 #3713. MR 250479
 9.
 R. A. Tapia, The weak Newton method and boundary value problems, SIAM J. Numer. Anal. 6 (1969), 539550. 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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Additional Information
DOI:
http://dx.doi.org/10.1090/S000299041974135032
PII:
S 00029904(1974)135032
