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Gill, Philip E.; Murray, Walter

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

Math. Program. 7, 311-350 (1974).
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Cited in 2 Reviews
Cited in 109 Documents

MSC:

90C30 Nonlinear programming
65K05 Numerical mathematical programming methods
49M15 Newton-type methods
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\textit{P. E. Gill} and \textit{W. Murray}, Math. Program. 7, 311--350 (1974; Zbl 0297.90082)
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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
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