# Optimality conditions for non-finite valued convex composite functions

Article

- Received:
- Revised:

DOI: 10.1007/BF01581075

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

- 31 Citations
- 143 Downloads

## 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

90C30 90C20 65K05 49A52 49B99### Key words

Convex composite functions second-order optimality conditions constraint qualification## Copyright information

© The Mathematical Programming Society, Inc. 1992