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

MSC:
90C30 Nonlinear programming
49M15 Newton-type methods
65K05 Numerical mathematical programming methods
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[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
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