×

An implementation of recursive quadratic programming variable metric methods for linearly constrained nonlinear minimax approximation. (English) Zbl 0548.90061

The paper contains a description of three algorithms for linearly constrained nonlinear minimax approximation. These algorithms use a dual method for solving quadratic programming subproblems together with variable metric updates for the Hessian matrix of the Lagrangian function. Moreover, a new line search procedure is described which is shown efficient in connection with a basic algorithm. The efficiency of all algorithms is demonstrated on test problems.

MSC:

90C30 Nonlinear programming
65K05 Numerical mathematical programming methods
49J35 Existence of solutions for minimax problems
49M37 Numerical methods based on nonlinear programming
90C20 Quadratic programming

Citations:

Zbl 0548.00061
PDF BibTeX XML Cite
Full Text: EuDML

References:

[1] R. M. Chamberlain M. J. D. Powell C. Lemarechal, H. C. Pedersen: The watchdog technique for forcing convergence in algorithms for constrained optimization. Math. Programming Study 16 (1982), 1 - 17. · Zbl 0477.90072
[2] R. Fletcher: The calculation of feasible points for linearly constrained optimisation problems. A.E.R.E. Harwell Report No. R-6354 (1970).
[3] R. Fletcher: Second order corrections for non-differentiable optimization. Numerical Analysis, Dundee 1981 (G. A. Watson, Lecture Notes in Mathematics 912, Springer-Verlag, Berlin 1982. · Zbl 0476.65048
[4] P. E. Gill, W. Murray: Safeguarded steplength algorithms for optimization using descent methods. National Physical Lab. Report No. NAC-37 (1974).
[5] S. P. Han: Variable metric methods for minimizing a class of nondifferentiable functions. Math. Programming 20 (1981), 1, 1-13. · Zbl 0441.90095
[6] L. Lukšan: Software package for optimization and nonlinear approximation. Proc. of the 2nd IFAC/IFIP Symposium on Software for Computer Control, Prague 1979.
[7] 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. · Zbl 0552.90074
[8] L. Lukšan: A compact variable metric algorithm for linearly constrained nonlinear minimax approximation. Kybernetika 21 (1985), to appear. · Zbl 0594.90078
[9] M. J. D. Powell: A fast algorithm for nonlinearly constrained optimization calculations. Numerical Analysis, Dundee 1977 (G. A. Watson, Lecture Notes in Mathematics 630, Springer-Verlag, Berlin 1978. · Zbl 0374.65032
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.