C. Wu and H. Wynn. The convergence of general step{length algorithms for regular optimum design criteria. Annals of Statistics, 6(6):1273-1285, 1978. Home/Search Document Not in Database Summary Related Articles Check |
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Sequential Experimental Design And Response Optimisation - Pronzato, Thierry (2000) (Correct)
....the same proof as in [20] applies. 2.2. L optimum penalty. Using an idea similar to previous section, one can relate the penalty function to L optimum design; that is, use (2.5) d k (x) d L k (x) r (x)M 1 k HM 1 k r(x) in (1.5) with H a non negative de nite matrix. It is shown in [23] that when H is positive de nite and the sequence fx k g is generated by x k 1 = arg maxx2X d L k (x) the design measure k converges to a L optimum design measure L that minimises trace H I 1 ( where I( R X r(x)r (x) dx) Further work is required to check if a property ....
C. Wu and H. Wynn. The convergence of general step{length algorithms for regular optimum design criteria. Annals of Statistics, 6(6):1273-1285, 1978.
Variational Calculus in Space of Measures and Optimal Design - Molchanov, Zuyev (2000) (1 citation) (Correct)
.... obtained by minimising D ( The steepest descent algorithm described in Section 3 emerges from our theoretical results on constrained optimisation in the space of measures presented in Section 1. In contrast to the classical sequential algorithms in the optimal design literature (Wu, 1978ab; Wu and Wynn, 1978; Wynn, 1970) we do not renormalise the obtained design measure on each step. Instead, the algorithm adds a signed measure chosen so to minimise the Fr echet derivative of the goal function among all measures satisfying the imposed constraints. This extends the ideas of ....
....obtained by minimising D ( The steepest descent algorithm described in Section 3 emerges from our theoretical results on constrained optimisation in the space of measures presented in Section 1. In contrast to the classical sequential algorithms in the optimal design literature (Wu, 1978ab; Wu and Wynn, 1978; Wynn, 1970) we do not renormalise the obtained design measure on each step. Instead, the algorithm adds a signed measure chosen so to minimise the Fr echet derivative of the goal function among all measures satisfying the imposed constraints. This extends the ideas of Atwood (1973, 1976) ....
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Wu, C.-F. and Wynn, H. P. (1978). The convergence of general step-length algorithms for regular optimum design criteria. Ann. Statist., 6:1273--1285.
Steepest Descent Algorithms in Space of Measures - Molchanov, Zuyev (2000) (Correct)
....for having a single atom placed at a point of global minimum 8 of d f ( Since this descent di ers from the steepest descent given in Corollary 3. 2, an additional analysis is necessary to ensure that the algorithm of the described kind does converge to the desired solution, see, e.g. [20]. The descent algorithm below is based on the arguments above and have been programmed in the SPLUS and R languages. The corresponding library medea (for MEasure DEscent Ascent) and related examples described in the next section can be obtained from the authors web pages. Procedure go.renorm ....
C.-F. Wu and H. P. Wynn. The convergence of general step-length algorithms for regular optimum design criteria. Ann. Statist., 6:1273-1285, 1978.
Optimal Design of Experiments for Modeling Processes with.. - Xu, Nair (1999) (1 citation) (Correct)
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Wu, C. F. J. and Wynn, H. P. (1978). The Convergence of General Step-length Algorithm for Regular Optimum Design Criteria. Ann. Statist. 6, 1273--1285.
Constrained Optimization of Experimental Design - Cook, Fedorov (1995) (4 citations) (Correct)
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Wu, C.F. and Wynn, H. (1978). The Convergence of General Step--Length Algorithms for Regular Optimum Design Criteria. Ann. Statist., 6, 1273--1285.
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