Sequential normal compactness in variational analysis

✍ Scribed by B.S. Mordukhovich; Bingwu Wang

• Publisher: Elsevier Science
• Year: 2001
• Tongue: English
• Weight: 591 KB
• Volume: 47
• Category: Article
• ISSN: 0362-546X
• DOI: 10.1016/s0362-546x(01)00217-6

✦ Synopsis

The paper is devoted to the study of the so-called sequential normal compactness conditions in variational analysis in infinite-dimensional spaces. Such conditions are needed for many aspects of generalized differentiation, particularly for calculus rules involving normal cones to sets, subdifferentials of nonsmooth functions, and coderivatives of set-valued mappings. These conditions automatically hold in finite-dimensional spaces and reveal one of the most principal differences between finite-dimensional and infinitedimensional variational theories. However, up to now it was not investigated how such conditions behave under various operations with sets, functions, and multifunctions. In this paper we address these questions and present new results that establish an efficient calculus of sequential normal compactness in a fairly general setting.