# Optimality conditions for non-finite valued convex composite functions

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DOI: 10.1007/BF01581075

- Cite this article as:
- Burke, J.V. & Poliquin, R.A. Mathematical Programming (1992) 57: 103. doi:10.1007/BF01581075

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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.

### AMS Subject Classifications

90C3090C2065K0549A5249B99### Key words

Convex composite functionssecond-order optimality conditionsconstraint qualification## Copyright information

© The Mathematical Programming Society, Inc. 1992