Frame Based Methods for Unconstrained Optimization

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

doi:10.1023/a:1026429319405

Cited by 86 publications

(67 citation statements)

References 5 publications

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“…A convergence analysis cannot properly be addressed in such a short paper as this but note that questions of convergence can be analyzed either by enforcing an appropriate trust region framework [6, §9.4] or by imposing some extra requirements on the choice of points used in the inner iterations, together with a careful choice of rule for modifying the mesh size parameter h, which is more in line with the framework described in [2,3]. It is not necessary for V to converge to the matrix of eigenvectors of ∇ 2 f in order to establish convergence to a stationary point but the use of second order information through V and D may provide a mechanism for establishing convergence to a stationary point satisfying second order necessary conditions.…”

Section: Discussionmentioning

confidence: 99%

Parallel Jacobi methods for derivative-free optimization on parallel or distributed processors

Coope

Macklem²

2005

ANZIAMJ

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New Jacobi-type algorithms are presented for the efficient use of parallel and distributed computing platforms in solving derivativefree optimization problems. The implementations are designed to be fault tolerant to be applicable to science and engineering problems where occasionally requests for function values may not be met and derivatives are never available. Convergence is usually achieved by introducing an elementary trust region subproblem at synchronization steps in the algorithm. This has the added advantage of handling negative curvature very conveniently.

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Section: Discussionmentioning

confidence: 99%

Parallel Jacobi methods for derivative-free optimization on parallel or distributed processors

Coope

Macklem²

2005

ANZIAMJ

Self Cite

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“…This set of trial points is called a frame. Less general than the frames of Coope and Price [8], the MADS frame uses the current incumbent solution x k (the frame center ) and the poll and mesh size parameters, ∆ p k > 0 and ∆ m k > 0, respectively, and a positive spanning set of…”

Section: Mesh Adaptive Direct Search (Mads)mentioning

confidence: 99%

Characteristic Shape Sequences for Measures on Images

Pinge¹,

Abramson²,

Asaki³

et al. 2006

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Researchers in many fields often need to quantify the similarity between images using metrics that measure qualities of interest in a robust quantitative manner. We present here the concept of image dimension reduction through characteristic shape sequences. We formulate the problem as a nonlinear optimization program and demonstrate the solution on a test problem of extracting maximal area ellipses from twodimensional image data. To solve the problem numerically, we augment the class of mesh adaptive direct search (MADS) algorithms with a filter, so as to allow infeasible starting points and to achieve better local solutions. Results here show that the MADS filter algorithm is successful in the test problem of finding good characteristic ellipse solutions from simple but noisy images.

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“…When either the SEARCH or the POLL step is successful, then the mesh size parameter is either kept constant or increased. Otherwise, when both steps fail to generate an unfiltered point, the incumbent is declared to be a mesh local optimizer [21] and the mesh size parameter is decreased.…”

Section: The Poll Stepmentioning

confidence: 99%

“…This may seem simple, but it is a crucial observation. Coope and Price [21,22,23] extended this notion to the idea of frames, which can be thought of as doing away with the requirement that the POLL points be mesh neighbors. Audet and Dennis [13] suggested MADS as a way to implement frames so that the directions used in infinitely many POLL steps generate a dense set in the tangent cone at a MADS limit pointx ∈ X.…”

Section: Introduction -The Problem and Its Propertiesmentioning

confidence: 99%

Nonlinear Programming by Mesh Adaptive Direct Searches

Abramson¹,

Audet²,

Dennis³

2005

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This paper is intended not as a survey, but as an introduction to some ideas behind the class of mesh adaptive direct search (MADS) methods. Space limitations dictate a brief description of various key topics to be provided along with several references, which themselves provide further references.The convergence theory for the methods presented here make a case for closing the gap between nonlinear optimizers and nonsmooth analysts. However these methods are certainly not of purely theoretical interest; they are successful on difficult practical problems. To encourage further use, we give references to available implementations. MADS is implemented in the direct search portion of the MathWorks MATLAB Genetic Algorithm and Direct Search (GADS) Toolbox.

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Frame Based Methods for Unconstrained Optimization

Cited by 86 publications

References 5 publications

Parallel Jacobi methods for derivative-free optimization on parallel or distributed processors

Parallel Jacobi methods for derivative-free optimization on parallel or distributed processors

Characteristic Shape Sequences for Measures on Images

Nonlinear Programming by Mesh Adaptive Direct Searches

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