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Optimally conditioned optimization algorithms without line searches.(English)Zbl 0328.90055


MSC:

90C30 Nonlinear programming
65K05 Numerical mathematical programming methods

Cite

References:

[1]M.J. Box, ”A comparison of several current optimization methods”,The Computer Journal 9 (1966) 67–77. ·Zbl 0146.13304
[2]K.W. Brodlie, A.R. Gourlay and J. Greenstadt, ”Rank one and two corrections to positive definite matrices expressed in product form”,Journal of the Institute of Mathematics and its Applications 11 (1973) 73–82. ·Zbl 0252.15007 ·doi:10.1093/imamat/11.1.73
[3]C.G. Broyden, ”The convergence of a class of double-rank minimization algorithms”,Journal of the Institute of Mathematics and its Applications 6 (1970) 76–90. ·Zbl 0223.65023 ·doi:10.1093/imamat/6.1.76
[4]W.C. Davidon, ”Variable metric method for minimization”, Argonne National Laboratory Rept. ANL-5990 (Rev.) (1959). ·Zbl 0752.90062
[5]L.C.W. Dixon, ”Quasi-Newton algorithms generate identical points”,Mathematical Programming 2 (1972) 383–387. ·Zbl 0245.65029 ·doi:10.1007/BF01584554
[6]A.V. Fiacco and G.P. McCormick,Nonlinear programming (Wiley, New York, 1968) p. 167. ·Zbl 0193.18805
[7]R. Fletcher and M.J.D. Powell, ”A rapidly convergent descent method for minimization”,The Computer Journal 6 (1963) 163–168. ·Zbl 0132.11603
[8]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
[9]D. Goldfarb, ”A family of variable metric methods derived by variationalmeans”,Mathematics of Computation 24 (1970) 23–26. ·Zbl 0196.18002 ·doi:10.1090/S0025-5718-1970-0258249-6
[10]H.Y. Huang, ”Unified approach to quadratically convergent algorithms for function minimization”,Journal of Optimization Theory and Application 5 (1970) 405–423. ·doi:10.1007/BF00927440
[11]H.J. Kelley and G.E. Myers, ”Conjugate direction methods for parameter optimization”,Astronautica Acta 16 (1971) 45–51. ·Zbl 0232.65052
[12]M.J.D. Powell, ”An iterative method for finding stationary values of a function of several variables”,The Computer Journal 5 (1962) 147–151. ·Zbl 0104.34303
[13]H.H. Rosenbrock, ”An automatic method for finding the greatest or least value of a function”,The Computer Journal 3 (1960) 175–184. ·doi:10.1093/comjnl/3.3.175
[14]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
[15]E. Spedicato, ”Conditioning in Huang’s two parameter class for conjugate gradients”, Centro Informazioni Studi Esperienze CISE-N-154.
[16]P. Wolfe, ”Another variable metric method”, working paper (1967). ·Zbl 0153.02401
[17]G. Zoutendijk,Methods of feasible directions (Elsevier, Amsterdam, 1960). ·Zbl 0097.35408
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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