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Lukšan, Ladislav

Variable metric methods for a class of extended conic functions. (English) Zbl 0548.90062

Kybernetika 21, 96-107 (1985).
The paper contains a description and an analysis of two variable metric algorithms for unconstrained minimization which find a minimum of an extended conic function after a finite number of steps provided it is possible to compute the derivatives of the model function at an arbitrary point \(x\in R_ n\). Moreover, the developed theory is applied to a special class of the exponential type of extended conic functions.

Cited in 1 Document

MSC:

90C30 Nonlinear programming
49M37 Numerical methods based on nonlinear programming
65K05 Numerical mathematical programming methods

Keywords:

finite step convergence; variable metric algorithms; unconstrained minimization; extended conic functions
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\textit{L. Lukšan}, Kybernetika 21, 96--107 (1985; Zbl 0548.90062)
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References:

[1] P. Bjørstad, J. Nocedal: Analysis of a new algorithm for one-dimensional minimization. Computing 22 (1979), 2, 93-100.
[2] C. G. Broyden: Quasi-Newton methods and their application to function minimization. Math. Comp. 21 (1967), 99, 368-381. · Zbl 0155.46704
[3] W. C. Davidon: Conic approximations and collinear scalings for optimizers. SIAM J. Numer. Anal. 77 (1980), 2, 268-281. · Zbl 0424.65026
[4] L. Lukšan: Quasi-Newton methods without projections for unconstrained minimization. Kybernetika 18 (1982), 4, 290-306. · Zbl 0514.65047
[5] L. Lukšan: Conjugate gradient algorithms for conic functions. Computing · Zbl 0622.65045
[6] D. C. Sorensen: The Q-superlinear convergence of a collinear scaling algorithm for unconstrained optimization. SIAM J. Numer. Anal. 77 (1980), I, 84-114. · Zbl 0428.65040
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.