Graphical Convergence of Set-Valued Maps

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WP-87-083.pdf

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WP-87-083.pdf

http://eprints.org/relation/isVersionOf https://pure.iiasa.ac.at/id/document/3009 http://eprints.org/relation/isVolatileVersionOf https://pure.iiasa.ac.at/id/document/3009 http://eprints.org/relation/isCoversheetVersionOf https://pure.iiasa.ac.at/id/document/3009 archive 351 disk0/00/00/29/69 2016-01-15 01:57:50 2021-08-27 17:12:58 2016-01-15 01:57:50 monograph show 2 Aubin J.-P. 7347 Graphical Convergence of Set-Valued Maps pub iis_met iis_mod prog_sds This is an introduction to graphical convergence of set-valued maps and the epigraphical convergence of extended real-valued functions. It is now well established that maps and, more generally, set-valued maps should be regarded not only as maps from one space to another, but should be characterized in an intrinsic and symmetric way by their graphs. When dealing with limits of maps, either single-valued or set-valued, it is quite advantageous to overcome the natural reluctance to handle convergence of subsets and to replace pointwise convergence by "graphical convergence": Instead of studying (more or less uniform) limits of the images, one consider the limits of their graphs. One of the main reasons is that doing so is that a map and its inverse are treated on the same footing. This is quite important in approximation theory and numerical analysis. The concepts of graphical convergence of set-valued maps are related to the concepts of epigraphical limits of functions, which had recently met an important success to overcome the failure of pointwise convergence in many problems of calculus of variations, optimization. stochastic programming. etc. Finally, this report provides a first study of the Kuratowski upper and lower limits of tangent cones, which is needed to compute generalized derivatives and epi-derivatives of graphical and epigraphical limits of maps and functions. 1987-09 published WP-87-083 WP-87-083 10 1134 public working_paper IIASA, Laxenburg, Austria 59 FALSE info:eu-repo/semantics/book