zbMATH — the first resource for mathematics

OPTAC: A portable software package for analyzing and comparing optimization methods by visualization. (English) Zbl 0857.65066
The authors discuss an interesting technique to visualize various minimization methods. Their technique is very useful to better understand convergence – whether a minimization method converges at all, how fast it converges, to which minimum it converges based on initial values, etc. The visualization technique introduced is applicable to visualizing the behavior of minimization methods for functions in \(n\) variables.
The paper should be of interest for anyone concerned with multivariate optimization, convergence, and, in particular, visualization of mathematical algorithms.

65K05 Numerical mathematical programming methods
90C30 Nonlinear programming
68U05 Computer graphics; computational geometry (digital and algorithmic aspects)
65Y15 Packaged methods for numerical algorithms
OPTAC; minpack
Full Text: DOI
[1] Armijo, L., Minimization of functions having Lipschitz continuous first partial derivatives, Pacific J. math., 16, 1-3, (1966) · Zbl 0202.46105
[2] Botsaris, C.A., A curvilinear optimization method based upon iterative estimation of the eigensystem of the Hessian matrix, J. math. anal. appl., 63, 396-411, (1978) · Zbl 0383.49024
[3] Dennis, J.E.; Schnabel, R.B., Numerical methods for unconstrained optimization and nonlinear equations, (1983), Prentice-Hall Englewood Cliffs, NJ · Zbl 0579.65058
[4] Kearfott, B., An efficient degree-computation method for a generalized method of bisection, Numer. math., 32, 109-127, (1979) · Zbl 0386.65016
[5] Luenberger, D.G., Introduction to linear and nonlinear programming, (1973), Addison-Wesley Reading, MA · Zbl 0241.90052
[6] MorĂ©, B.J.; Garbow, B.S.; Hillstrom, K.E., Testing unconstrained optimization, ACM trans. math. software, 7, 17-41, (1981) · Zbl 0454.65049
[7] Ortega, J.M.; Rheinboldt, W.C., Iterative solution of nonlinear equations in several variables, (1970), Academic Press New York · Zbl 0241.65046
[8] Press, W.H.; Teukolsky, S.A.; Vetterling, W.T.; Flannery, B.P., Numerical recipes, the art of scientific computing, (1992), Cambridge University Press New York · Zbl 0845.65001
[9] Stenger, F., Computing the topological degree of a mapping in Rn, Numer. math., 25, 23-38, (1975) · Zbl 0316.55007
[10] Vrahatis, M.N., Solving systems of nonlinear equations using the nonzero value of the topological degree, ACM trans. math. software, 14, 312-329, (1988) · Zbl 0665.65052
[11] Vrahatis, M.N.; Androulakis, G.S.; Manoussakis, G.E., A new unconstrained optimization method for imprecise function and gradient values, J. math. anal. appl., 197, 586-607, (1996) · Zbl 0887.90166
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.