Publication:
Set-Convergence and Its Application: A Tutorial

dc.contributor.authorRoyset, Johannes O.
dc.contributor.departmentOperations Research (OR)
dc.date.accessioned2020-08-07T23:15:26Z
dc.date.available2020-08-07T23:15:26Z
dc.date.issued2020-02
dc.description.abstractOptimization problems, generalized equations, and the multitude of other variational problems invariably lead to the analysis of sets and set-valued mappings as well as their approximations. We review the central concept of set-convergence and explain its role in defining a notion of proximity between sets, especially for epigraphs of functions and graphs of set-valued mappings. The development leads to an approximation theory for optimization problems and generalized equations with profound consequences for the construction of algorithms. We also introduce the role of setconvergence in variational geometry and subdifferentiability with applications to optimality conditions. Examples illustrate the importance of set-convergence in stability analysis, error analysis, construction of algorithms, statistical estimation, and probability theory.en_US
dc.description.funderThis work is supported by ONR (Operations Research) under N0001420WX00519 and AFOSR (Optimization and Discrete Mathematics) under F4FGA08272G001.en_US
dc.description.sponsorshipThis work is supported by ONR (Operations Research) under N0001420WX00519 and AFOSR (Optimization and Discrete Mathematics) under F4FGA08272G001.en_US
dc.format.extent14 p.
dc.identifier.citationRoyset, Johannes O. "Set-Convergence and Its Application: A Tutorial." arXiv preprint arXiv:2002.09774 (2020).
dc.identifier.urihttps://hdl.handle.net/10945/65314
dc.publisherArXiven_US
dc.rightsThis publication is a work of the U.S. Government as defined in Title 17, United States Code, Section 101. Copyright protection is not available for this work in the United States.en_US
dc.subject.authorset-convergenceen_US
dc.subject.authorepi-convergenceen_US
dc.subject.authorgraphical convergenceen_US
dc.subject.authorweak convergenceen_US
dc.subject.authorstabilityen_US
dc.subject.authorapproximation theoryen_US
dc.subject.authorvariational geometryen_US
dc.subject.authorsubdifferentiabilityen_US
dc.subject.authortruncated Hausdorff distanceen_US
dc.titleSet-Convergence and Its Application: A Tutorialen_US
dc.typePreprinten_US
dspace.entity.typePublication
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