A Convergent Variant of the Nelder–Mead Algorithm

Price, C. J.; Coope, I. D.; Byatt, D.

doi:10.1023/a:1014849028575

Cited by 114 publications

(99 citation statements)

References 10 publications

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“…This is in the spirit of several of the early direct search methods such as Rosenbrock's method of rotating directions [227], Powell's method based on conjugate directions [213], and the adaptive simplex of Nelder and Mead [194]. The algorithmic strategies in the former two papers, in particular, informed the developments in [76,77,224].…”

Section: And αmentioning

confidence: 97%

Optimization by Direct Search: New Perspectives on Some Classical and Modern Methods

2003

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Abstract. Direct search methods are best known as unconstrained optimization techniques that do not explicitly use derivatives. Direct search methods were formally proposed and widely applied in the 1960s but fell out of favor with the mathematical optimization community by the early 1970s because they lacked coherent mathematical analysis. Nonetheless, users remained loyal to these methods, most of which were easy to program, some of which were reliable. In the past fifteen years, these methods have seen a revival due, in part, to the appearance of mathematical analysis, as well as to interest in parallel and distributed computing. This review begins by briefly summarizing the history of direct search methods and considering the special properties of problems for which they are well suited. Our focus then turns to a broad class of methods for which we provide a unifying framework that lends itself to a variety of convergence results. The underlying principles allow generalization to handle bound constraints and linear constraints. We also discuss extensions to problems with nonlinear constraints.

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Section: And αmentioning

confidence: 97%

Optimization by Direct Search: New Perspectives on Some Classical and Modern Methods

2003

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“…Due to the difference in the acquisition frequency between the camera and the measurement arm, the pose assigned to an image was interpolated from the two nearest neighbors using linear interpolation for the translational part and spherical interpolation for the rotational part. We used the NelderMead algorithm [15] to jointly optimize t o f f set and T ext for each sequence, starting with t o f f set = 0 and with the result of the manual registration for T ext .…”

Section: Post-processing the Dataset Acquisitionmentioning

confidence: 99%

A dataset and evaluation methodology for template-based tracking algorithms

Lieberknecht

Benhimane²,

Meier³

et al. 2009

2009 8th IEEE International Symposium on Mixed and Augmented Reality

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Unlike dense stereo, optical flow or multi-view stereo, templatebased tracking lacks benchmark datasets allowing a fair comparison between state-of-the-art algorithms. Until now, in order to evaluate objectively and quantitatively the performance and the robustness of template-based tracking algorithms, mainly synthetically generated image sequences were used. The evaluation is therefore often intrinsically biased.In this paper, we describe the process we carried out to perform the acquisition of real scene image sequences with very precise and accurate ground truth poses using an industrial camera rigidly mounted on the end-effector of a high-precision robotic measurement arm. For the acquisition, we considered most of the critical parameters that influence the tracking results such as: the texture richness and the texture repeatability of the objects to be tracked, the camera motion and speed, and the changes of the object scale in the images and variations of the lighting conditions over time.We designed an evaluation scheme for object detection and interframe tracking algorithms and used the image sequences to apply this scheme to several state-of-the-art algorithms. The image sequences will be made freely available for testing, submitting and evaluating new template-based tracking algorithms, i.e. algorithms that detect or track a planar object in an image sequence given only one image of the object (called the template).

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“…Also, it has recently been shown that in some cases the N M method will not converge, as in McKinnon [7]. More complicated variants have been developed (see for example Price et al [11]) that guarantee convergence. However, none of these difficulties occurred here, and the standard NM method was acceptable.…”

Section: The Nelder-mead Downhill Simplex Methodsmentioning

confidence: 99%

“…https://doi.org/10.1017/S1446181100013456 [11] Maximising output from oil reservoirs without water breakthrough …”

Section: Non-negative Nelder-mead On the Feasible Boundarymentioning

confidence: 99%

Maximising output from oil reservoirs without water breakthrough

Lucas

2004

ANZIAM J.

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Often in oil reservoirs a layer of water lies under the layer of oil. The suction pressure due to a distribution of oil wells will cause the oil-water interface to rise up towards the wells. Given a particular distribution of oil wells, we are interested in finding the flow rates of each well that maximise the total flow rate without the interface breaking through to the wells. A method for finding optimal flow rates is developed using the Muskat model to approximate the interface height, and a version of the Nelder-Mead simplex method for optimisation. A variety of results are presented, including the perhaps nonintuitive result that it is better to turn off some oil wells when they are sufficiently close to one another.

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A Convergent Variant of the Nelder–Mead Algorithm

Cited by 114 publications

References 10 publications

Optimization by Direct Search: New Perspectives on Some Classical and Modern Methods

Optimization by Direct Search: New Perspectives on Some Classical and Modern Methods

A dataset and evaluation methodology for template-based tracking algorithms

Maximising output from oil reservoirs without water breakthrough

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