eprintid: 4683 rev_number: 6 eprint_status: archive userid: 351 dir: disk0/00/00/46/83 datestamp: 2016-01-15 02:06:51 lastmod: 2021-08-27 17:36:14 status_changed: 2016-01-15 02:06:51 type: article metadata_visibility: show item_issues_count: 1 creators_name: Mordukhovich, B.S. creators_name: Shao, Y. creators_id: 7482 title: Nonconvex differential calculus for infinite dimensional multifunctions ispublished: pub internal_subjects: iis_met internal_subjects: iis_mod divisions: prog_dyn abstract: The paper is concerned with generalized differentiation of set-valued mappings between Banach spaces. Our basic object is the so-called coderivative of multifunctions that was introduced earlier by the first author and has had a number of useful applications to nonlinear analysis, optimization, and control. This coderivative is a nonconvex-valued mapping which is related to sequential limits of Fréchet-like graphical normals but is not dual to any tangentially generated derivative of multifunctions. Using a variational approach, we develop a full calculus for the coderivative in the framework of Asplund spaces. The latter class is sufficiently broad and convenient for many important applications. Some useful calculus results are also obtained in general Banach spaces. date: 1996 date_type: published publisher: Springer id_number: 10.1007/BF00419366 iiasapubid: XJ-96-018 creators_browse_id: 1461 full_text_status: none publication: Set-Valued Analysis volume: 4 number: 3 pagerange: 205-236 refereed: TRUE issn: 0927-6947 coversheets_dirty: FALSE fp7_type: info:eu-repo/semantics/article citation: Mordukhovich, B.S. & Shao, Y. (1996). Nonconvex differential calculus for infinite dimensional multifunctions. Set-Valued Analysis 4 (3) 205-236. 10.1007/BF00419366 .