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Related Publications
(7)
On the Convergence of DerivativeFree Methods for Unconstrained Optimization
A direct search optimization method that models the objective and constraint functions by linear interpolation
Approximation concepts for optimum structural design — a review
Recent progress in unconstrained nonlinear optimization without derivatives
Design and Analysis of Computer Experiments
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An algorithm using quadratic interpolation for unconstrained derivative free optimization
An algorithm using quadratic interpolation for unconstrained derivative free optimization,A. R. Conn,P. L. Toint
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An algorithm using quadratic interpolation for unconstrained derivative free optimization
(
Citations: 44
)
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A. R. Conn
,
P. L. Toint
Published in 1996.
Cumulative
Annual
Citation Context
(21)
...The general structure of UOBYQA follows a modelbased approach [4,
5
], which constructs a chain of local quadratic models that approximate the objective function...
...A general framework of this approach is given by Conn and Toint in [
5
], and convergence analysis is presented in [4]...
Geng Deng
,
et al.
VariableNumber SamplePath Optimization
...The general structure of UOBYQA follows a modelbased approach (
Conn and Toint 1996
), which constructs a chain of local quadratic models to approximate the objective function within certain trust regions (Nocedal and Wright 2006)...
Punit Prakash
,
et al.
Design optimization of a robust sleeve antenna for hepatic microwave a...
...For the purpose of reducing computation time, Conn et al. [
5
] proposed to use Newton fundamental polynomial function for constructing the model...
...S for reducing the value k'( ˆ X)¡1k by some suitable method (see [
5
] for details)...
...Conn and Toint claim that the modelbased algorithm is robust for small errors in objective function from numerical results in [
5
, 7], in which the errors was generated in uniformly random number...
Jun TAKAKI
.
A DerivativeFree TrustRegion Algorithm for Unconstrained Optimizatio...
...There is also a related class of “global modeling methods” that use design of interpolation models [
1
,6,7]...
S. Z. Hassan
,
et al.
Quadratic Interpolation Algorithm for Minimizing Tabulated Function
... approximate the objective function locally and hence are likely to approximate it better than a global model would, they are generated using a relatively small number of points (relevant for expensive functions), they are efficiently minimized by gradientbased algorithms and they retain their goodness in the presence of noise thanks to the interpolation technique used and since, being quadratic, they smooth out noise fluctuations [3,
10
, ...
...The quadratic model functions are generated by interpolation [8,
10
, 33, 42, 43]...
...A linear polynomial was found to be inferior to a quadratic one [32, 34], while polynomials of degree higher than two [
10
] were rejected since they may require more interpolation points which is undesirable when function evaluations are expensive, and since they may contain oscillations [3]...
Yoel Tenne
,
et al.
A Memetic Algorithm Using a TrustRegion DerivativeFree Optimization ...
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Citations
(44)
VariableNumber SamplePath Optimization
(
Citations: 10
)
Geng Deng
,
Michael C. Ferris
Journal:
Mathematical Programming
, vol. 117, no. 12, pp. 81109, 2009
Selfcorrecting geometry in modelbased algorithms for derivativefree unconstrained optimization
(
Citations: 3
)
K. Scheinberg
,
L. Toint
Published in 2009.
Design optimization of a robust sleeve antenna for hepatic microwave ablation
(
Citations: 7
)
Punit Prakash
,
Geng Deng
,
Mark C Converse
,
John G Webster
,
David M Mahvi
,
Michael C Ferris
Journal:
Physics in Medicine and Biology  PHYS MED BIOL
, vol. 53, no. 4, pp. 10571069, 2008
A DerivativeFree TrustRegion Algorithm for Unconstrained Optimization with Controllable Error
(
Citations: 1
)
Jun TAKAKI
Published in 2008.
Quadratic Interpolation Algorithm for Minimizing Tabulated Function
S. Z. Hassan
,
Y. A. ElRewaily
Journal:
Journal of Mathematics and Statistics
, vol. 4, no. 4, pp. 217221, 2008