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Optimality conditions for nonfinite valued convex composite functions
 J. V. Burke,
 R. A. Poliquin
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Burke (1987) has recently developed secondorder necessary and sufficient conditions for convex composite optimization in the case where the convex function is finite valued. In this note we present a technique for reducing the infinite valued case to the finite valued one. We then use this technique to extend the results in Burke (1987) to the case in which the convex function may take infinite values. We conclude by comparing these results with those established by Rockafellar (1989) for the piecewise linearquadratic case.
Dedicated to the memory of Robin W. Chaney
Research supported in part by the National Science Foundation under grants DMS8602399 and DMS8803206, and by the Air Force Office of Scientific Research under grant ISSA860080.
Research supported in part by the Natural Sciences and Engineering Research Council of Canada under grant OGP41983.
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 Title
 Optimality conditions for nonfinite valued convex composite functions
 Journal

Mathematical Programming
Volume 57, Issue 13 , pp 103120
 Cover Date
 19920501
 DOI
 10.1007/BF01581075
 Print ISSN
 00255610
 Online ISSN
 14364646
 Publisher
 SpringerVerlag
 Additional Links
 Topics
 Keywords

 90C30
 90C20
 65K05
 49A52
 49B99
 Convex composite functions
 secondorder optimality conditions
 constraint qualification
 Industry Sectors
 Authors

 J. V. Burke ^{(1)}
 R. A. Poliquin ^{(2)}
 Author Affiliations

 1. Department of Mathematics, GN50, University of Washington, 98195, Seattle, WA, USA
 2. Department of Mathematics, University of Alberta, T6G 2G1, Edmonton, Alberta, Canada