×

zbMATH — the first resource for mathematics

An ODE-based approach to nonlinearly constrained minimax problems. (English) Zbl 0824.65039
The paper presents an algorithm for solving a standard nonlinear programming problem (optimization problem with a finite number of equality-inequality constraints and smooth data). Each iteration of the algorithm solves approximately a system of nonlinear ordinary differential equations to get a direction for the line search. The authors claim that their code is more robust, although slower, than several library routines.
MSC:
65K05 Numerical mathematical programming methods
90C30 Nonlinear programming
Software:
CONMAX
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] J. Angelos, M. Henry, E. Kaufman Jr., and T. Lenker, Optimal nodes for polynomial interpolation, (presented at theSixth International Symposium on Approximation Theory, College Station, Texas, 1989), inApproximation Theory VI, vol. 1, eds C.K. Chui, L.L. Schumaker, and J.D. Ward (Academic Press, San Diego, 1989) pp. 17–20.
[2] A. Brown and M. Bartholomew-Biggs, ODE vs. SQP methods for constrained optimisation, Technical Report #179, the Hatfield Polytechnic Optimisation Centre (June, 1987).
[3] C. Dunham and C. Zhu, Best approximation with approximations nonlinear in a few variables, Congr. Numer. 87 (1992) (Proc. Manitoba Conf. on Numerical Math. and Computing) pp. 203–220. · Zbl 0778.41011
[4] R. Fletcher,Practical Methods of Optimization, 2nd ed. (John Wiley and Sons, 1987). · Zbl 0905.65002
[5] E. Kaufman and G. Taylor, Approximation and interpolation by convexity preserving rational splines, to appear in Constr. Approx. · Zbl 0807.41009
[6] K. Schittkowski,More Test Examples for Nonlinear Programming Codes, Lecture Notes in Economics and Mathematical Systems no. 282, (Springer-Verlag, New York, 1987). · Zbl 0658.90060
[7] P. Wolfe, Finding the nearest point in a polytope, Math. Progr. 11 (1976) 128–149. · Zbl 0352.90046 · doi:10.1007/BF01580381
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.