Gradient-only approaches to avoid spurious local minima in unconstrained optimization

dc.contributor.authorWilke, Daniel Nicolas
dc.contributor.authorKok, Schalk
dc.contributor.authorSnyman, Johannes Arnoldus
dc.contributor.authorGroenwold, Albert A.
dc.contributor.emailnico.wilke@up.ac.zaen_US
dc.date.accessioned2014-05-12T10:51:03Z
dc.date.available2014-05-12T10:51:03Z
dc.date.issued2013
dc.description.abstractWe 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.description.librarianhb2014en_US
dc.description.sponsorshipNational Research Foundation (NRF)en_US
dc.description.urihttp://link.springer.com/journal/11081en_US
dc.identifier.citationWilke, DN, Kok, S, Snyman, JA & Groenwold, AA 2013, 'Gradient-only approaches to avoid spurious local minima in unconstrained optimization', Optimization and Engineering, vol. 14, no. 2, pp. 275-304.en_US
dc.identifier.issn1389-4420 (print)
dc.identifier.issn1573-2924 (online)
dc.identifier.other10.1007/s11081-011-9178-7
dc.identifier.urihttp://hdl.handle.net/2263/39764
dc.language.isoenen_US
dc.publisherSpringeren_US
dc.rights© Springer Science+Business Media, LLC 2011.The original publication is available at : http://link.springer.com/journal/11081en_US
dc.subjectStep discontinuousen_US
dc.subjectGradient-only optimizationen_US
dc.subjectUnconstrained optimizationen_US
dc.subjectPartial differential equationsen_US
dc.subjectVariable discretization strategiesen_US
dc.subjectShape optimizationen_US
dc.titleGradient-only approaches to avoid spurious local minima in unconstrained optimizationen_US
dc.typePostprint Articleen_US

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