We discuss the following question: for a function $f$ of two or more variables which is convex in the directions of coordinate axes, what can its trace $g\left(x\right)=f(x,x,...,x)$ 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.

Accepted:

DOI: 10.1051/cocv/2016066

Keywords: Separately convex function, trace problem

^{1}; Pokorný, Dušan

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@article{COCV_2017__23_4_1617_0, author = {Kurka, Ond\v{r}ej and Pokorn\'y, Du\v{s}an}, title = {Notes on the trace problem for separately convex functions}, journal = {ESAIM: Control, Optimisation and Calculus of Variations}, pages = {1617--1648}, publisher = {EDP-Sciences}, volume = {23}, number = {4}, year = {2017}, doi = {10.1051/cocv/2016066}, zbl = {1390.26023}, mrnumber = {3716935}, language = {en}, url = {http://archive.numdam.org/articles/10.1051/cocv/2016066/} }

TY - JOUR AU - Kurka, Ondřej AU - Pokorný, Dušan TI - Notes on the trace problem for separately convex functions JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2017 SP - 1617 EP - 1648 VL - 23 IS - 4 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/cocv/2016066/ DO - 10.1051/cocv/2016066 LA - en ID - COCV_2017__23_4_1617_0 ER -

%0 Journal Article %A Kurka, Ondřej %A Pokorný, Dušan %T Notes on the trace problem for separately convex functions %J ESAIM: Control, Optimisation and Calculus of Variations %D 2017 %P 1617-1648 %V 23 %N 4 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/cocv/2016066/ %R 10.1051/cocv/2016066 %G en %F COCV_2017__23_4_1617_0

Kurka, Ondřej; Pokorný, Dušan. Notes on the trace problem for separately convex functions. ESAIM: Control, Optimisation and Calculus of Variations, Volume 23 (2017) no. 4, pp. 1617-1648. doi : 10.1051/cocv/2016066. http://archive.numdam.org/articles/10.1051/cocv/2016066/

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