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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
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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.

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Keywords: Successive approximation, constrained optimization, convergence, convex analysis, dual operations, subdifferentials, infimal convolution, conjugate duality, separable functions
Article copyright: © Copyright 1981 American Mathematical Society