A compact variable metric algorithm for linearly constrained nonlinear minimax approximation

Ladislav Lukšan

Kybernetika (1985)

  • Volume: 21, Issue: 6, page 405-427
  • ISSN: 0023-5954

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Lukšan, Ladislav. "A compact variable metric algorithm for linearly constrained nonlinear minimax approximation." Kybernetika 21.6 (1985): 405-427. <http://eudml.org/doc/29039>.

@article{Lukšan1985,
author = {Lukšan, Ladislav},
journal = {Kybernetika},
keywords = {linearly constrained nonlinear minimax approximation; product-form variable metric updates},
language = {eng},
number = {6},
pages = {405-427},
publisher = {Institute of Information Theory and Automation AS CR},
title = {A compact variable metric algorithm for linearly constrained nonlinear minimax approximation},
url = {http://eudml.org/doc/29039},
volume = {21},
year = {1985},
}

TY - JOUR
AU - Lukšan, Ladislav
TI - A compact variable metric algorithm for linearly constrained nonlinear minimax approximation
JO - Kybernetika
PY - 1985
PB - Institute of Information Theory and Automation AS CR
VL - 21
IS - 6
SP - 405
EP - 427
LA - eng
KW - linearly constrained nonlinear minimax approximation; product-form variable metric updates
UR - http://eudml.org/doc/29039
ER -

References

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  1. K. W. Brodlie A. R. Gourlay, and J. Greenstadt, Rank one and two corrections to positive definite matrices expressed in product form, J. Inst. Math. Appl. 11 (1973), 1, 73 - 82. (1973) MR0331770
  2. R. Fletcher, The calculation of feasible points for linearly constrained optimization problems, A.E.R.E. Harwell Rept. No. R-6354 (1970). (1970) 
  3. P. E. Gill, W. Murray, A numerically stable form of the simplex algorithm, Linear Algebra Appl. 7 (1973), 2,99-138. (1973) Zbl0255.65029MR0321519
  4. P. E. Gill, W. Murray, Newton-type methods for unconstrained and linearly constrained optimization, Math. Programming 7 (1974), 3, 311 - 350. (1974) Zbl0297.90082MR0356503
  5. S. P. Han, Variable metric methods for minimizing a class of nondifferentiable functions, Math. Programming 20 (1981), 1, 1-13. (1981) Zbl0441.90095MR0594019
  6. L. Lukšan, Software package for optimization and nonlinear approximation, Proc. of the 2nd IFAC/IFIP Symposium on Software for Computer Control, Prague 1979. (1979) 
  7. L. Lukšan, Quasi-Newton methods without projections for linearly constrained minimization, Kybernetika 18 (1982), 4, 307-319. (1982) MR0688369
  8. L. Lukšan, Variable metric methods for linearly constrained nonlinear minimax approximation, Computing 30 (1983), 3, 315-334. (1983) MR0706672
  9. L. Lukšan, Dual method for solving a special problem of quadratic programming as a sub-problem at linearly constrained nonlinear minimax approximation, Kybernetika 20 (1984), 6, 445-457. (1984) MR0777979
  10. L. Lukšan, A compact variable metric algorithm for nonlinear minimax approximation, Computing (to appear). MR0843944
  11. L. Lukšan, An implementation of recursive quadratic programming variable metric methods for linearly constrained nonlinear minimax approximation, Kybernetika 21 (1985), 1, 22-40. (1985) MR0788667
  12. K. Madsen, H. Schjaer-Jacobsen, Linearly constrained minimax optimization, Math. Programming 14 (1978), 2, 208-223. (1978) Zbl0375.65034MR0472055
  13. M. J. D. Powell, A fast algorithm for nonlinearly constrained optimization calculations, In: Numerical Analysis, Dundee 1977 (G. A. Watson, ed.), Lecture Notes in Mathematics 630, Springer-Verlag, Berlin 1978. (1977) MR0483447
  14. K. Ritter, A variable metric method for linearly constrained minimization problems, In: Nonlinear Programming 3 (O. L. Mangasarian, R. R. Meyer and S. M. Robinson, eds.), Academic Press, London 1978. (1978) Zbl0464.65041MR0507864
  15. P. Wolfe, Finding the nearest point in a polytope, Math. Programming 11 (1976), 2, 128-149. (1976) Zbl0352.90046MR0452683

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