zbMATH — the first resource for mathematics

Optimal conditioning of self-scaling variable metric algorithms. (English) Zbl 0342.90045

90C30 Nonlinear programming
49M15 Newton-type methods
65K05 Numerical mathematical programming methods
Full Text: DOI
[1] R. Fletcher, ”A new approach to variable metric algorithms”,The Computer Journal 13 (1970) 317–322. · Zbl 0207.17402 · doi:10.1093/comjnl/13.3.317
[2] A.A. Goldstein, ”On steepest descent”,SIAM Journal on Control 1 (1965) 147–151. · Zbl 0221.65094
[3] H.Y. Huang, ”Unified approach to quadratically convergent algorithms for function minimization”,Journal of Optimization Theory and Applications 5 (1970) 405–423. · Zbl 0194.19402 · doi:10.1007/BF00927440
[4] S.S. Oren, ”Self-scaling variable metric algorithms for unconstrained minimization”, Ph.D. thesis, Department of Engineering-Economic Systems, Stanford University, Stanford, Calif., 1972.
[5] S.S. Oren and D.G. Luenberger, ”Self-scaling variable metric (SSVM) algorithms I: criteria and sufficient conditions for scaling a class of algorithms”,Management Science 20 (1974) 845–862. · Zbl 0316.90064 · doi:10.1287/mnsc.20.5.845
[6] S.S. Oren, ”Self-scaling variable metric (SSVM) algorithms II: implementation and experiments”,Management Science 20 (1974) 863–874. · Zbl 0316.90065 · doi:10.1287/mnsc.20.5.863
[7] S.S. Oren, ”Self-scaling variable metric algorithm without linesearch for unconstrained minimization”,Mathematics of Computation 27 (1973) 873–885. · Zbl 0304.65045 · doi:10.1090/S0025-5718-1973-0329259-8
[8] S.S. Oren, ”On the selection of parameters in self-scaling variable metric algorithms”, PARC Memo Rept., ARG MR# 73-8 (Presented at the 8th International Symposium on Mathematical Programming, Stanford, August 1973).
[9] D.F. Shanno and P.C. Kettler, ”Optimal conditioning of quasi-Newton methods”,Mathematics of Computation 24 (1970) 657–667. · Zbl 0225.65074 · doi:10.1090/S0025-5718-1970-0274030-6
[10] E. Spedicato, ”Stability of Huang’s update for the conjugate gradient method”,Journal of Optimization Theory and Applications 11 (1973) 469–479. · Zbl 0254.49034 · doi:10.1007/BF00935660
[11] E. Spedicato, ”On condition numbers of matrices in rank two minimization algorithms”, CISE Rept., CISE, Segrete, Italy. · Zbl 0339.90053
[12] E. Spedicato, ”A bound on the condition number of rank-two corrections and applications to the variable metric methods”,Mathematics to Computation, to appear. · Zbl 0318.65029
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.