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Newton-type methods for unconstrained and linearly constrained optimization.(English)Zbl 0297.90082


MSC:

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

Cite

References:

[1]R.H. Bartels, G.H. Golub and M.A. Saunders, ”Numerical techniques in mathematical programming”, in: J.B. Rosen, O.L. Mangasarian and K. Ritter, eds.,Nonlinear programming (Academic Press, New York, 1970) pp. 123–176. ·Zbl 0228.90030
[2]K.M. Brown and J.E. Dennis, Jr., ”Derivative-free analogues of the Levenberg–Marquardt and Gauss algorithms for non-linear least squares approximation”,Numerische Mathematik 18 (1972) 289–297. ·Zbl 0235.65043 ·doi:10.1007/BF01404679
[3]P. Businger and G.H. Golub, ”Linear least squares solutions by Householder transformations”,Numerische Mathematik 7 (1965) 269–276. ·Zbl 0142.11503 ·doi:10.1007/BF01436084
[4]A.R. Curtis, M.J.D. Powell and J.K. Reid, ”On the estimation of sparse Jacobian matrices”,Journal of the Institute of Mathematics and its Applications 13 (1974) 117–119. ·Zbl 0273.65036
[5]A.V. Fiacco and G.P. McCormick,Nonlinear programming: sequential unconstrained minimization techniques (Wiley, New York, 1968). ·Zbl 0193.18805
[6]P.E. Gill, G.H. Golub, W. Murray and M.A. Saunders, ”Methods for modifying matrix factorizations”,Mathematics of Computation 28 (1974) 505–535. ·Zbl 0289.65021 ·doi:10.1090/S0025-5718-1974-0343558-6
[7]P.E. Gill and W. Murray, ”Quasi-Newton methods for unconstrained optimization”,Journal of the Institute of Mathematics and its Applications 9 (1972) 91–108. ·Zbl 0264.49026 ·doi:10.1093/imamat/9.1.91
[8]P.E. Gill and W. Murray, ”A numerically stable form of the simplex algorithm”,Linear Algebra and its Applications 7 (1973) 99–138. ·Zbl 0255.65029 ·doi:10.1016/0024-3795(73)90047-5
[9]P.E. Gill and W. Murray, ”The numerical solution of a problem in the calculus of variations”, in: D.J. Bell, ed.,Recent mathematical developments in control (Academic Press, New York, 1973) pp. 97–122.
[10]P.E. Gill and W. Murray, ”Quasi-Newton methods for linearly constrained optimization”, National Physical Laboratory Rept. NAC 32 (1973).
[11]P.E. Gill and W. Murray, ”Safeguarded steplength algorithms for optimization using descent methods”, National Physical Laboratory Rept. NAC 37 (1974).
[12]P.E. Gill, W. Murray and S.M. Picken, ”The implementation of two modified Newton algorithms for unconstrained optimization”, National Physical Laboratory Rept. NAC 24 (1972).
[13]P.E. Gill, W. Murray and S.M. Picken, ”The implementation of two modified Newton algorithms for linearly constrained optimization”, to appear.
[14]P.E. Gill, W. Murray and R.A. Pitfield, ”The implementation of two revised quasi-Newton algorithms for unconstrained optimization”, National Physical Laboratory Rept. NAC 11 (1972).
[15]A. Goldstein and J. Price, ”An effective algorithm for minimization”,Numerische Mathematik 10 (1967) 184–189. ·Zbl 0161.35402 ·doi:10.1007/BF02162162
[16]J. Greenstadt, ”On the relative efficiencies of gradient methods”,Mathematics of Computation 21 (1967) 360–367. ·Zbl 0159.20305 ·doi:10.1090/S0025-5718-1967-0223073-7
[17]R.S. Martin, G. Peters and J.H. Wilkinson, ”Symmetric decomposition of a positive-definite matrix”,Numerische Mathematik 7 (1965) 362–383. ·Zbl 0135.37402 ·doi:10.1007/BF01436249
[18]A. Matthews and D. Davies, ”A comparison of modified Newton methods for unconstrained optimization”,Computer Journal 14 (1971) 213–294. ·Zbl 0224.65020 ·doi:10.1093/comjnl/14.3.293
[19]G.P. McCormick, ”A second-order method for the linearly constrained non-linear programming problem”, in: J.B. Rosen, O.L. Mangasarian and K. Ritter, eds.,Nonlinear programming (Academic Press, New York, 1970) pp. 207–243.
[20]W. Murray, ”An algorithm for finding a local minimum of an indefinite quadratic program” National Physical Laboratory Rept. NAC 1 (1971).
[21]W. Murray, ”Second derivative methods”, in: W. Murray, ed.,Numerical methods for unconstrained optimization (Academic Press, New York, 1972) pp. 107–122.
[22]J.M. Ortega and W.C. Rheinboldt,Iterative solution of non-linear equations in several variables (Academic Press, New York, 1970). ·Zbl 0241.65046
[23]J. Stoer, ”On the numerical solution of constrained least square problems”,SIAM Journal on Numerical Analysis 8 (1971) 382–411. ·Zbl 0219.90039 ·doi:10.1137/0708038
[24]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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