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Local convergence analysis for partitioned quasi-Newton updates.(English)Zbl 0505.65018


MSC:

65K05 Numerical mathematical programming methods
65H10 Numerical computation of solutions to systems of equations
90C30 Nonlinear programming

Software:

ve08

Cite

References:

[1]Dennis, J.E., Moré, J.J.: Quasi-Newton Methods, Motivation and Theory. SIAM Rev.19, 46-89 (1977) ·Zbl 0356.65041 ·doi:10.1137/1019005
[2]Dennis, J.E., Moré, J.J.: A Characterization of Superlinear Convergence and Its Application to Quasi-Newton Methods. Math. Comput.28 (126), 549-560 (1974) ·Zbl 0282.65042 ·doi:10.1090/S0025-5718-1974-0343581-1
[3]Dembo, R.S., Eisenstat, S.C., Steilhaug, T.: Inexact-Newton Methods. SIAM J. Numer. Anal.19, 400-408 (1982) ·Zbl 0478.65030 ·doi:10.1137/0719025
[4]Dennis, J.E., Walker, H.F.: Convergence Theorems for Least Change Secant Update Methods. SIAM J. Numer. Anal.18, 949-987 (1981) ·Zbl 0527.65032 ·doi:10.1137/0718067
[5]Fletcher, R.: A New Approach to Variable Metric Algorithms. Comput. J.13, 317-322 (1970) ·Zbl 0207.17402 ·doi:10.1093/comjnl/13.3.317
[6]Griewank, A., Toint, Ph.L.: Partitioned Variable Metric Updates for Large Structured Optimization Problems. Numer. Math.39, 119-137 (1982) ·Zbl 0482.65035 ·doi:10.1007/BF01399316
[7]Griewank, A., Toint, Ph.L.: On the Unconstrained Optimization of Partially separable Functions. In M.J.D. Powell (ed.), Nonlinear Optimization. New York: Academic Press, 1981 ·Zbl 0563.90085
[8]Ortega, J.M., Rheinboldt, W.C.: Iterative Solution of Nonlinear Equations in Several Variables. New York: Academic Press, 1970 ·Zbl 0241.65046
[9]Powell, M.J.D.: Some Global Convergence Properties of a Variable Metric Algorithm for Minimization Without Exact Line Searches. SIAM-AMS Proc.9. ·Zbl 0338.65038
[10]Powell, M.J.D.: The convergence of variable metric methods for nonlinearly constrained optimization calculations In O.L. Mangasarin, R.R. Meyer, S.M. Robinson (ed.), Nonlinear Programming 3. New York: Academic Press, 1978 ·Zbl 0464.65042
[11]Ritter, K.: Local and Superlinear Convergence of a Class of Variable Metric Methods. Computing23, 287-297 (1979) ·Zbl 0447.65034 ·doi:10.1007/BF02252133
[12]Stachurski, A.: Superlinear Convergence of Broyden’s Bounded theta-Class of Methods. Math. Progr.20, 196-212 (1981) ·Zbl 0448.90048 ·doi:10.1007/BF01589345
[13]Steihaug, T.: Quasi-Newton Methods for Large Scale Nonlinear Problems. PhD Thesis, Yale University, 1980
[14]Stoer, J.: On the Convergence Rate of Imperfect Minimization Algorithms in Broyden’s beta-Class. Math. Progr.9 (3), 313-335 (1975) ·Zbl 0346.90047 ·doi:10.1007/BF01681353
[15]Warth, W., Werner, J.: Effizente Schrittweitenfunktionen bei unrestringierten Optimierungsaufgaben. Computing19 (1), 59-72 (1977) ·Zbl 0367.90101 ·doi:10.1007/BF02260741
[16]Werner, J.: Über die globale Konvergenz von Variable-Metrik Verfahren mit nichtexakter Schrittweitenbestimmung. Numer. Math.31, 321-334 (1978) ·Zbl 0427.65047 ·doi:10.1007/BF01397884
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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
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