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Matrix conditioning and nonlinear optimization.(English)Zbl 0371.90109


MSC:

90C30 Nonlinear programming

Cite

References:

[1]C.G. Broyden, ”Quasi-Newton methods and their application to functional minimization”,Mathematics of Computation 21 (1967) 368–381. ·Zbl 0155.46704 ·doi:10.1090/S0025-5718-1967-0224273-2
[2]C.G. Broyden, ”The convergence of a class of double rank minimization algorithms. 2. The new algorithm”,Journal of the Institute of Mathematics and its Applications 6 (1970) 222–231. ·Zbl 0207.17401 ·doi:10.1093/imamat/6.3.222
[3]W.C. Davidon, ”Optimally conditioned optimization algorithms without line searches”,Mathematical Programming 9 (1975) 1–30. ·Zbl 0328.90055 ·doi:10.1007/BF01681328
[4]J.E. Dennis and J. More, ”Quasi-Newton methods, motivation and theory”, Computer Science Report TR74-217, Cornell University (1974).
[5]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
[6]D. Goldfarb, ”A family of variable-metric method derived by variational means”,Mathematics of Computation 24 (1970) 23–26. ·Zbl 0196.18002 ·doi:10.1090/S0025-5718-1970-0258249-6
[7]D.H. Jacobson and W. Oksman, ”An algorithm that minimizes homogeneous functions ofn variables inN + 2 iterations and rapidly minimizes general functions”, Technical Report 618, Division of Engineering and Applied Physics, Harvard University, Cambridge, MA, (1970). ·Zbl 0202.16501
[8]G.P. McCormick and K. Ritter, ”Methods of conjugate directions versus quasi-Newton methods”,Mathematical Programming 3 (1972) 101–116. ·Zbl 0247.90055 ·doi:10.1007/BF01584978
[9]S.S. Oren, ”Self-scaling variable metric algorithm. Part II”,Management Science 20 (1974) 863–874. ·Zbl 0316.90065 ·doi:10.1287/mnsc.20.5.863
[10]S.S. Oren, ”On the selection of parameters in self-scaling variable metric algorithms”,Mathematical Programming 3 (1974) 351–367. ·Zbl 0297.90084 ·doi:10.1007/BF01585530
[11]S.S. Oren and D.G. Luenberger, ”Self-scaling variable metric algorithm. Part I”,Management Science 20 (1974) 845–862. ·Zbl 0316.90064 ·doi:10.1287/mnsc.20.5.845
[12]S.S. Oren and E. Spedicato, ”Optimal conditioning of self-scaling variable metric algorithms”,Mathematical Programming 10 (1976) 70–90. ·Zbl 0342.90045 ·doi:10.1007/BF01580654
[13]D.F. Shanno, ”Conditioning of quasi-Newton methods for function minimization”,Mathematics of Computation 24 (1970) 647–656. ·Zbl 0225.65073 ·doi:10.1090/S0025-5718-1970-0274029-X
[14]D.F. Shanno and K.H. Phua, ”Minimization of unconstrained multivariate functions”,TOMS 2 (1976) 87–94. ·Zbl 0319.65042 ·doi:10.1145/355666.355673
[15]E. Spedicato, ”Computational experience with quasi-Newton algorithms for minimization problems of moderately large size”, Report CISE-N-175, CISE Documentation Service, Segrate (Milano) (1975). ·Zbl 0397.90088
[16]D.F. Shanno and K.H. Phua, ”Numerical comparison of several variable metric algorithms”, MIS Tech. Rept 21, University of Arizona (1977).
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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