R. Fletcher [1990], Low storage methods for unconstrained optimization, Lectures in Applied Mathematics (AMS) 26, pp. 165-179. Home/Search Document Not in Database Summary Related Articles Check |
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Large Scale Unconstrained Optimization - Nocedal (1996) (4 citations) (Correct)
....in this respect. 4.2.2 Current Research and Open Questions Wehavedevoted much attention so far to the L BFGS method, but this may not be the most economical limited memory method. New algorithms designed to reduce the amount of storage without compromising performance are proposed in[23] 60] [27] [43] see also [1] It is easy to see that if the BFGS method is started with an initial matrix that is a multiple of the identity,thens k 2 spanfg 0 #: #g k g. This suggests that there is some redundancy in storing both s i and y i in a limited memory method, and in most of the recent proposals ....
R. Fletcher (1990). Low storage methods for unconstrained optimization, Computational Solutions of Nonlinear Systems of Equations, eds.E.L.Allgower and K. Georg, Lectures in Applied Mathematics 26, AMS Publications, Providence, RI.
Large Scale Unconstrained Optimization - Nocedal (1996) (4 citations) (Correct)
....in this respect. 4.2.2 Current Research and Open Questions We have devoted much attention so far to the L BFGS method, but this may not be the most economical limited memory method. New algorithms designed to reduce the amount of storage without compromising performance are proposed in [23] 60] [27], 43] see also [1] It is easy to see that if the BFGS method is started with an initial matrix that is a multiple of the identity, then s k 2 spanfg 0 ; g k g. This suggests that there is some redundancy in storing both s i and y i in a limited memory method, and in most of the recent ....
R. Fletcher (1990). Low storage methods for unconstrained optimization, Computational Solutions of Nonlinear Systems of Equations, eds. E. L. Allgower and K. Georg, Lectures in Applied Mathematics 26, AMS Publications, Providence, RI.
On the Asymptotic Behaviour of some New Gradient Methods - Dai, Fletcher (2003) Self-citation (Fletcher) (Correct)
....numerical experience on problems up to 10 variables, showing that the resulting algorithm compares reasonably well against the Polak Ribi ere and CONMIN techniques. Due to its simplicity and eciency, the BB method now has received many useful and successful generalizations and applications, see [2, 3, 4, 7, 9, 11, 12, 14, 17, 18, 19], etc. Moreover, the numerical experiments in [7] for unconstrained optimization show that the AS method is a promising alternative to the BB method. Despite the good numerical performance of the BB and CSDS methods, very little is known about their asymptotic behaviour, except in the case n = 2. ....
R. Fletcher, Low storage methods for unconstrained optimization, Lectures in Applied Mathematics (AMS) 26 (1999), pp. 165-179.
On the Barzilai-Borwein method - Fletcher (2001) (2 citations) Self-citation (Fletcher) (Correct)
....for n = 2, the method converges R superlinearly. Barzilai and Borwein also show that their method is considerably superior to the classical steepest descent method for one instance of a quadratic function with Barzilai Borwein method 3 n = 4, but no other numerical results are given. Fletcher ([8], 1990) investigates some connections with the spectrum of A in the quadratic case, and an ingenious proof by Raydan ( 21] 1993) demonstrates convergence in the quadratic case. However, neither of these papers gives any numerical results and the method attracted little attention until a seminal ....
R. Fletcher, Low storage methods for unconstrained optimization, Lectures in Applied Mathematics (AMS) 26, (1990), pp. 165-179.
An Overview of Unconstrained Optimization - Fletcher (1993) (6 citations) Self-citation (Fletcher) (Correct)
....definite H (k) without any restriction other than ffi (k) T fl (k) 0, it is not likely to be improved upon significantly. Some recent work has looked at the possibility of limited memory algorithms which store only one n Theta m matrix and not two as in (3.16) and (3. 17) Fletcher [22] describes a method in which B (k) is represented as B (k) h S fi fi fi S i S T S T (3:20) omitting superscript k) where S 2 IR n Thetak and columns of S form an orthonormal basis for the null space of S. The BFGS method (with B (1) I) can then be expressed as ....
Fletcher R. (1990) Low storage methods for unconstrained optimization, in Computational Solution of Nonlinear Systems of Equations, eds. E.L.Allgower and K.Georg, Lectures in Applied Mathematics Vol. 26, AMS Publications, Providence, RI.
Inexact Spectral Projected Gradient Methods on Convex Sets - Birgin, Martinez, Raydan (2003) (Correct)
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R. Fletcher [1990], Low storage methods for unconstrained optimization, Lectures in Applied Mathematics (AMS) 26, pp. 165-179.
Inexact Spectral Projected Gradient Methods on Convex Sets - Birgin, Martinez, Raydan (2003) (Correct)
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R. Fletcher [1990], Low storage methods for unconstrained optimization, Lectures in Applied Mathematics (AMS) 26, pp. 165--179.
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