Differential Calculus of Set-Valued Maps. An Update

2959 31 2999 4 5958 document 2999 WP-87-093.pdf application/pdf f2a74145667f74d7250530bbf97e31c9 MD5 2055623 2016-01-15 01:57:47 https://pure.iiasa.ac.at/id/eprint/2959/1/WP-87-093.pdf 2959 1 1 text en public

WP-87-093.pdf

22 3aaa56698043a65894ad67063c7017d4f26d8b06 18721 2 30451 document 18721 lightbox.jpg image/png 430f4e8846a2c085b6b45d3f48c0e1d7 MD5 11769 2016-01-15 13:24:57 https://pure.iiasa.ac.at/id/eprint/2959/2/lightbox.jpg 2959 2 2 image/png other Thumbnails conversion from text to thumbnail_lightbox en public

lightbox.jpg

preview.jpg

medium.jpg

small.jpg

indexcodes.txt

WP-87-093.pdf

http://eprints.org/relation/isVersionOf https://pure.iiasa.ac.at/id/document/2999 http://eprints.org/relation/isVolatileVersionOf https://pure.iiasa.ac.at/id/document/2999 http://eprints.org/relation/isCoversheetVersionOf https://pure.iiasa.ac.at/id/document/2999 archive 351 disk0/00/00/29/59 2016-01-15 01:57:47 2021-08-27 17:12:57 2016-01-15 01:57:47 monograph show 2 Aubin J.-P. 7347 Differential Calculus of Set-Valued Maps. An Update pub iis_met prog_sds IIASA has played a crucial role in the development of the "graphical approach" to the differential calculus of set-valued maps, around J.-P. Aubin, H. Frankowska, R.T. Rockafellar and allowed to make contacts with Soviet and eastern European mathematicians (C. Olech, B. Pschenichnyiy, E. Polovinkin, V. Tihomirov, etc.) who were following analogous approaches. Since 1981, they and their collaborators developed this calculus and applied it to a variety of problems, in mathematical programming (Kuhn-Tucker rules, sensitivity of solutions and Lagrange multipliers), in nonsmooth analysis (Inverse Functions Theorems, local uniqueness), in control theory (controllability of systems with feedbacks, Pontryagin's Maximum Principle, Hamilton-Jacobi-Bellman equations, observability and other issues), in viability theory (regulation of systems, heavy trajectories), etc. The first version of this survey appeared at IIASA in 1982, and constituted the seventh chapter of the book "Applied Nonlinear Analysis" published in 1984 by I. Ekeland and the author. Since then, many other results have been motivated by the successful applications of this calculus, and, maybe unfortunately, other concepts (such as the concept of intermediate tangent cone and derivatives introduced and used by H. Frankowska). Infinite-dimensional problems such as control problems or the more classical problems of calculus of variations require the use of adequate adaptations of the same main idea, as well as more technical assumptions. The time and the place (IIASA) were ripe to update the exposition of this differential calculus. The Russian translation of "Applied Nonlinear Analysis" triggered this revised version. 1987-09 published WP-87-093 WP-87-093 10 1134 public working_paper IIASA, Laxenburg, Austria 84 FALSE info:eu-repo/semantics/book