dc.contributor.author |
Wilke, DN
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|
dc.contributor.author |
Kok, S
|
|
dc.contributor.author |
Snyman, JA
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|
dc.contributor.author |
Groenwold, AA
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|
dc.date.accessioned |
2013-11-28T06:22:10Z |
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dc.date.available |
2013-11-28T06:22:10Z |
|
dc.date.issued |
2013-06 |
|
dc.identifier.citation |
Wilke, D.N, Kok, S, Snyman, J.A and Groenwold, A.A. 2013. Gradient-only approaches to avoid spurious local minima in unconstrained optimization. Optimization and Engineering, vol. 14(2), pp 275-304 |
en_US |
dc.identifier.issn |
1389-4420 |
|
dc.identifier.uri |
http://link.springer.com/article/10.1007%2Fs11081-011-9178-7
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|
dc.identifier.uri |
http://hdl.handle.net/10204/7108
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|
dc.description |
Copyright: 2013 Springer. This is an ABSTRACT ONLY. The definitive version is published in Optimization and Engineering, vol. 14(2), pp 275-304 |
en_US |
dc.description.abstract |
We reflect on some theoretical aspects of gradient-only optimization for the unconstrained optimization of objective functions containing non-physical step or jump discontinuities. This kind of discontinuity arises when the optimization problem is based on the solutions of systems of partial differential equations, in combination with variable discretization techniques (e.g. remeshing in spatial domains, and/or variable time stepping in temporal domains). These discontinuities, which may cause local minima, are artifacts of the numerical strategies used and should not influence the solution to the optimization problem. Although the discontinuities imply that the gradient field is not defined everywhere, the gradient field associated with the computational scheme can nevertheless be computed everywhere; this field is denoted the associated gradient field. We demonstrate that it is possible to overcome attraction to the local minima if only associated gradient information is used. Various gradient-only algorithmic options are discussed. A salient feature of our approach is that variable discretization strategies, so important in the numerical solution of partial differential equations, can be combined with efficient local optimization algorithms. |
en_US |
dc.language.iso |
en |
en_US |
dc.publisher |
Springer |
en_US |
dc.relation.ispartofseries |
Workflow;11778 |
|
dc.subject |
Step discontinuous |
en_US |
dc.subject |
Gradient-only optimization |
en_US |
dc.subject |
Unconstrained optimization |
en_US |
dc.subject |
Partial differential equations |
en_US |
dc.subject |
Variable discretization strategies |
en_US |
dc.subject |
Shape optimization |
en_US |
dc.title |
Gradient-only approaches to avoid spurious local minima in unconstrained optimization |
en_US |
dc.type |
Conference Presentation |
en_US |
dc.identifier.apacitation |
Wilke, D., Kok, S., Snyman, J., & Groenwold, A. (2013). Gradient-only approaches to avoid spurious local minima in unconstrained optimization. Springer. http://hdl.handle.net/10204/7108 |
en_ZA |
dc.identifier.chicagocitation |
Wilke, DN, S Kok, JA Snyman, and AA Groenwold. "Gradient-only approaches to avoid spurious local minima in unconstrained optimization." (2013): http://hdl.handle.net/10204/7108 |
en_ZA |
dc.identifier.vancouvercitation |
Wilke D, Kok S, Snyman J, Groenwold A, Gradient-only approaches to avoid spurious local minima in unconstrained optimization; Springer; 2013. http://hdl.handle.net/10204/7108 . |
en_ZA |
dc.identifier.ris |
TY - Conference Presentation
AU - Wilke, DN
AU - Kok, S
AU - Snyman, JA
AU - Groenwold, AA
AB - We reflect on some theoretical aspects of gradient-only optimization for the unconstrained optimization of objective functions containing non-physical step or jump discontinuities. This kind of discontinuity arises when the optimization problem is based on the solutions of systems of partial differential equations, in combination with variable discretization techniques (e.g. remeshing in spatial domains, and/or variable time stepping in temporal domains). These discontinuities, which may cause local minima, are artifacts of the numerical strategies used and should not influence the solution to the optimization problem. Although the discontinuities imply that the gradient field is not defined everywhere, the gradient field associated with the computational scheme can nevertheless be computed everywhere; this field is denoted the associated gradient field. We demonstrate that it is possible to overcome attraction to the local minima if only associated gradient information is used. Various gradient-only algorithmic options are discussed. A salient feature of our approach is that variable discretization strategies, so important in the numerical solution of partial differential equations, can be combined with efficient local optimization algorithms.
DA - 2013-06
DB - ResearchSpace
DP - CSIR
KW - Step discontinuous
KW - Gradient-only optimization
KW - Unconstrained optimization
KW - Partial differential equations
KW - Variable discretization strategies
KW - Shape optimization
LK - https://researchspace.csir.co.za
PY - 2013
SM - 1389-4420
T1 - Gradient-only approaches to avoid spurious local minima in unconstrained optimization
TI - Gradient-only approaches to avoid spurious local minima in unconstrained optimization
UR - http://hdl.handle.net/10204/7108
ER -
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en_ZA |