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Newton's method for convex programming and Tchebycheff approximation

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References

  1. Remez, E.: Sur un, Procédé Convergent d'Approximations Successives pour Determiner les Polynomes d'Appproximation. C. R. Acad. Sci. Paris198, 2063–2065 (1934).

    Google Scholar 

  2. Remez, E.: Sur le Calcul Effectif des Polynomes d'Approximation deTschebyscheff. C. R. Acad. Sci. Paris199, 337–340 (1934).

    Google Scholar 

  3. Remez, E. Ya.: On the Method of Best, in the Sense ofTchebycheff, Approximate Representation of Functions, (Ukrainian), Kiev, 1935. See also Reference 4 below.

  4. Remez, E. Ya. General Computation Methods for Chebyshev Approximation. Problems with Real Parameters Entering Linearly. Izdat. Akad. Nauk Ukrainsk. SSR. Kiev, 1957. 454 pp. See also MR 19-580 (Russian).

  5. Novodvorskii, E. N., andI. Sh. Pinsker: On a Process of Equalization of Maxima, Uspehi Matem. Nauk, N. S.6, 174–181 (1951). See alsoShenitzer, A.: Chebyshev Approximations. J. Assoc. Comput. Mach.4, 30–35 (1957). MR 13-728.

    Google Scholar 

  6. Beale, E. M. L.: An Alternative Method for Linear Programming. Proc. Cambridge Philos. Soc.50, 512–523 (1954). MR 16-155.

    Google Scholar 

  7. Beale, E. M. L.: On Minimizing, a Convex Function Subject to Linear Inequalities. J. Roy. Stat. Soc., Ser. B17, 173–177 (1955).

    Google Scholar 

  8. Bratton, Donald: New Results in the Theory and Techniques of Chebyshev Fitting. Abstract 546-34. Notices Am. Math. Soc.5, 248 (1958).

    Google Scholar 

  9. Stiefel, Eduard L.: Numerical Methods of Tchebycheff Approximation, pp. 217–232 inR. E. Langer (ed.), On Numerical Approximation. Madison 1959. 480 pp.

  10. Stiefel, E.: Über diskrete und lineare Tschebyscheff-Approximationen. Numerische Mathematik1, 1–28 (1959).

    Google Scholar 

  11. Wolfe, Philip: Programming with Nonlinear Constraints. Preliminary Report, Abstract 548-102. Notices Am. Math. Soc.5, 508 (1958).

    Google Scholar 

  12. Stone, Jeremy J. The Cross Section Method, presented orally at Symposium for Mathematical Programming, RAND Corporation, March 19, 1959.

  13. Kelley, James E.: A General Technique for Convex Programming, presented orally at Symposium on Mathematical Programming, RAND Corporation, March 19, 1959.

  14. Cheney, E. W., andA. A. Goldstein: Proximity Maps for Convex Sets. Proc. Amer. Math. Soc.10, 448–450 (1959).

    Google Scholar 

  15. Bonnesen, T., u.W. Fenchel: Theorie der konvexen Körper. Berlin 1934.

  16. Fan, K.: On Systems of Linear Inequalities. In: Linear Inequalities and Related Systems, ed., byH. W. Kuhn andA. W. Tucker, pp. 99–156. Princeton 1956.

  17. Bram, Joseph: Chebychev Approximation in Locally Compact Spaces. Proc. Am. Math. Soc.9, 133–136 (1958).

    Google Scholar 

  18. Goldstein, A. A., andE. W. Cheney: A Finite Algorithm for the Solution of Consistent Linear Equations and Inequalities and for the Tchebycheff Approximation of Inconsistent Linear Equations. Pac. J. Math.8, 415–427 (1958).

    Google Scholar 

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Cheney, E.W., Goldstein, A.A. Newton's method for convex programming and Tchebycheff approximation. Numer. Math. 1, 253–268 (1959). https://doi.org/10.1007/BF01386389

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