Full entry |
PDF
(2.4 MB)
Feedback

nonlinear minimax approximation; method of recursive quadratic programming; dual method; convergence; algorithm

References:

[1] M. S. Bazaraa C. M. Shetty: **Nonlinear programming. Theory and algorithms**. New York: Wiley 1979. MR 0533477

[2] C. Charalambous J. W. Bandler: **Nonlinear minimax optimization as a sequence of least p-th optimization with finite values of p**. Faculty Engn., McMaster University, Hamilton, Ontario, Canada, Kept. SOC-3, 1973.

[3] C. Charalambous: **Acceleration of the least p-th algorithm for minimax optimization with engineering applications**. Math. Programming 17, 270-297, (1979). DOI 10.1007/BF01588251 | MR 0550846

[4] V. F. Demyanov V. N. Malozemov: **Introduction to minimax**. Chap. 3, § 5. New York: Wiley 1974. MR 0475823

[5] D. Goldfarb: **Extension of Davidon's variable metric method to maximization under linear inequality and equality constraints**. SIAM J. Appl. Math. 17, 739-764, (1969). DOI 10.1137/0117067 | MR 0290799 | Zbl 0185.42602

[6] D. Goldfarb A. U. Idnani: **A numerically stable dual method for solving strictly convex quadratic programs**. The City College of New York, Dept. of Computer Sci., Rept. 81- 102, (1981).

[7] J. Hald K. Madsen: **Combined LP and Quasi-Newton methods for minimax optimization**. Math. Programming 20, 49-62, (1981). DOI 10.1007/BF01589332 | MR 0594023

[8] S. P. Han: **Variable metric methods for minimizing a class of nondifferentiable functions**. Math. Programming 20, 1 - 13, (1981). MR 0594019 | Zbl 0441.90095

[9] L. Lukšan: **Variable metric methods for linearly constrained nonlinear minimax approximation**. Computing 30, 315-334, (1983). DOI 10.1007/BF02242138 | MR 0706672

[10] K. Madsen: **An algorithm for minimax solution of overdetermined systems of nonlinear equations**. J. Inst. Math. Appl. 16, 321-328, (1975). DOI 10.1093/imamat/16.3.321 | MR 0443341

[11] M. J. D. Powell: **A fast algorithm for nonlinearly constrained optimization calculations**. In "Numerical analysis, Dundes 1977", (G. A. Watson, ed.), Lecture Notes in Mathematics 630, Berlin: Springer-Verlag 1978. MR 0483447