Notes on the trace problem for separately convex functions
Optimization and Control
2017-10-24 v1 Classical Analysis and ODEs
Abstract
We discuss the following question: For a function f of two or more variables which is convex in the directions of coordinate axes, how can its trace g(x) = f(x, x, ..., x) look like? In the two-dimensional case, we provide some necessary and sufficient conditions, as well as some examples illustrating that our approach does not seem to be appropriate for finding a characterization in full generality. For a concave function g, however, a characterization in the two-dimensional case is established.
Keywords
Cite
@article{arxiv.1409.8477,
title = {Notes on the trace problem for separately convex functions},
author = {Ondřej Kurka and Dušan Pokorný},
journal= {arXiv preprint arXiv:1409.8477},
year = {2017}
}
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33 pages