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nonlinear minimax approximation; method of recursive quadratic programming; dual method; convergence; algorithm
The paper describes the dual method for solving a special problem of quadratic programming as a subproblem at nonlinear minimax approximation. Two cases are analyzed in detail, differring in linear dependence of gradients of the active functions. The complete algorithm of the dual method is presented and its finite step convergence is proved.
[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
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