Dual method for solving a special problem of quadratic programming as a subproblem at nonlinear minimax approximation

Ladislav Lukšan

Aplikace matematiky (1986)

  • Volume: 31, Issue: 5, page 379-395
  • ISSN: 0862-7940

Abstract

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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.

How to cite

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Lukšan, Ladislav. "Dual method for solving a special problem of quadratic programming as a subproblem at nonlinear minimax approximation." Aplikace matematiky 31.5 (1986): 379-395. <http://eudml.org/doc/15462>.

@article{Lukšan1986,
abstract = {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.},
author = {Lukšan, Ladislav},
journal = {Aplikace matematiky},
keywords = {nonlinear minimax approximation; method of recursive quadratic programming; dual method; convergence; algorithm; nonlinear minimax approximation; method of recursive quadratic programming; dual method; convergence},
language = {eng},
number = {5},
pages = {379-395},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Dual method for solving a special problem of quadratic programming as a subproblem at nonlinear minimax approximation},
url = {http://eudml.org/doc/15462},
volume = {31},
year = {1986},
}

TY - JOUR
AU - Lukšan, Ladislav
TI - Dual method for solving a special problem of quadratic programming as a subproblem at nonlinear minimax approximation
JO - Aplikace matematiky
PY - 1986
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 31
IS - 5
SP - 379
EP - 395
AB - 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.
LA - eng
KW - nonlinear minimax approximation; method of recursive quadratic programming; dual method; convergence; algorithm; nonlinear minimax approximation; method of recursive quadratic programming; dual method; convergence
UR - http://eudml.org/doc/15462
ER -

References

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  1. M. S. Bazaraa C. M. Shetty, Nonlinear programming. Theory and algorithms, New York: Wiley 1979. (1979) Zbl0476.90035MR0533477
  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. (1973) Zbl0349.90108
  3. C. Charalambous, 10.1007/BF01588251, Math. Programming 17, 270-297, (1979). (1979) Zbl0418.90072MR0550846DOI10.1007/BF01588251
  4. V. F. Demyanov V. N. Malozemov, Introduction to minimax, Chap. 3, § 5. New York: Wiley 1974. (1974) MR0475823
  5. D. Goldfarb, 10.1137/0117067, SIAM J. Appl. Math. 17, 739-764, (1969). (1969) Zbl0185.42602MR0290799DOI10.1137/0117067
  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). (1981) Zbl0537.90081
  7. J. Hald K. Madsen, 10.1007/BF01589332, Math. Programming 20, 49-62, (1981). (1981) Zbl0441.90097MR0594023DOI10.1007/BF01589332
  8. S. P. Han, Variable metric methods for minimizing a class of nondifferentiable functions, Math. Programming 20, 1 - 13, (1981). (1981) Zbl0441.90095MR0594019
  9. L. Lukšan, 10.1007/BF02242138, Computing 30, 315-334, (1983). (1983) Zbl0514.49016MR0706672DOI10.1007/BF02242138
  10. K. Madsen, 10.1093/imamat/16.3.321, J. Inst. Math. Appl. 16, 321-328, (1975). (1975) Zbl0355.65038MR0443341DOI10.1093/imamat/16.3.321
  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. (1977) Zbl0374.65032MR0483447

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