Geodesic
Notes on the trace problem for separately convex functions
Kurka, Ondřej1 ; Pokorný, Dušan1
1 Charles University, Faculty of Mathematics and Physics, Sokolovská 83, 186 75 Praha 8, Czech Republic.
ESAIM: Control, Optimisation and Calculus of Variations, Tome 23 (2017) no. 4, pp. 1617-1648

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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(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.

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Accepté le :
DOI : 10.1051/cocv/2016066
Classification : 26B25
Keywords: Separately convex function, trace problem

Kurka, Ondřej 1 ; Pokorný, Dušan 1

1 Charles University, Faculty of Mathematics and Physics, Sokolovská 83, 186 75 Praha 8, Czech Republic. 
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Kurka, Ondřej; Pokorný, Dušan. Notes on the trace problem for separately convex functions. ESAIM: Control, Optimisation and Calculus of Variations, Tome 23 (2017) no. 4, pp. 1617-1648. doi: 10.1051/cocv/2016066

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