Optimality conditions for non-finite valued convex composite functions |
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Authors: | J V Burke R A Poliquin |
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Institution: | (1) Department of Mathematics, GN-50, University of Washington, 98195 Seattle, WA, USA;(2) Department of Mathematics, University of Alberta, T6G 2G1 Edmonton, Alberta, Canada |
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Abstract: | Burke (1987) has recently developed second-order 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 linear-quadratic case.Dedicated to the memory of Robin W. ChaneyResearch supported in part by the National Science Foundation under grants DMS-8602399 and DMS-8803206, and by the Air Force Office of Scientific Research under grant ISSA-860080.Research supported in part by the Natural Sciences and Engineering Research Council of Canada under grant OGP41983. |
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Keywords: | 90C30 90C20 65K05 49A52 49B99 |
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