Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Preservation of convergence of convex sets and functions in finite dimensions


Authors: L. McLinden and Roy C. Bergstrom
Journal: Trans. Amer. Math. Soc. 268 (1981), 127-142
MSC: Primary 26B25; Secondary 65K10
MathSciNet review: 628449
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We study a convergence notion which has particular relevance for convex analysis and lends itself quite naturally to successive approximation schemes in a variety of areas. Motivated particularly by problems in optimization subject to constraints, we develop technical tools necessary for systematic use of this convergence in finite-dimensional settings. Simple conditions are established under which this convergence for sequences of sets, functions and subdifferentials is preserved under various basic operations, including, for example, those of addition and infimal convolution in the case of functions.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 26B25, 65K10

Retrieve articles in all journals with MSC: 26B25, 65K10


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1981-0628449-5
PII: S 0002-9947(1981)0628449-5
Keywords: Successive approximation, constrained optimization, convergence, convex analysis, dual operations, subdifferentials, infimal convolution, conjugate duality, separable functions
Article copyright: © Copyright 1981 American Mathematical Society