| 1. |
- Glad, Torkel, 1947-, et al.
(författare)
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A Multiplier Method with Automatic Limitation of Penalty Growth
- 1979
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Ingår i: Mathematical programming. - : Springer. - 0025-5610 .- 1436-4646. ; 17:1, s. 140-155
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Tidskriftsartikel (refereegranskat)abstract
- This paper presents a multiplier method for solving optimization problems with equality and inequality constraints. The method realizes all the good features that were foreseen by R. Fletcher for this type of algorithm in the past, but which suffers from none of the drawbacks of the earlier attempts.
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| 2. |
- Glad, Torkel, 1947-, et al.
(författare)
-
Optimization of Functions whose Values are Subject to Small Errors
- 1977
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Ingår i: BIT Numerical Mathematics. - : Kluwer Academic Publishers. - 0006-3835 .- 1572-9125. ; 17:2, s. 160-169
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Tidskriftsartikel (refereegranskat)abstract
- In this paper we consider the minimization of a function whose values can only be obtained with an error. For the case when the error has certain statistical properties this problem has been investigated by Kiefer and Wolfowitz (1) and Kushner (2, 3). Kushner has shown that a certain class of algorithms converge to a stationary point with probability one. Here a different approach is used. The error is assumed to have an upper bound and it is shown that a stationary point can be obtained to within a certain accuracy, dependent on the magnitude of the error. Our results are related to works concerning roundoff errors for one dimensional optimization (4) and solution of nonlinear equations (5). The algorithm we use can be regarded as an extension of the methods used in (6), (8) and (9).
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| 3. |
- Glad, Torkel, 1947-
(författare)
-
Properties of Updating Methods for the Multipliers in Augmented Lagrangians
- 1979
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Ingår i: Journal of Optimization Theory and Applications. - : Kluwer Academic Publishers. - 0022-3239 .- 1573-2878. ; 28:2, s. 135-156
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Tidskriftsartikel (refereegranskat)abstract
- The convergence properties of different updating methods for the multipliers in augmented Lagrangians are considered. It is assumed that the updating of the multipliers takes place after each line search of a quasi-Newton method. Two of the updating methods are shown to be linearly convergent locally, while a third method has superlinear convergence locally. Modifications of the algorithms to ensure global convergence are considered. The results of a computational comparison with other methods are presented.
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| 4. |
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