Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Sectional convexity of epigraphs of conjugate mappings with applications
  to robust vector duality   This paper concerns the robust vector problems \begin{equation*}
\mathrm{(RVP)}\ \ {\rm Wmin}\left\{ F(x): x\in C,\; G_u(x)\in -S,\;\forall
u\in\mathcal{U}\right\}, \end{equation*} where $X, Y, Z$ are locally convex
Hausdorff topological vector spaces, $K$ is a closed and convex cone in $Y$
with nonempty interior, and $S$ is a closed, convex cone in $Z$, $\mathcal{U}$
is an \textit{uncertainty set}, $F\colon X\rightarrow {Y}^\bullet,$ $G_u\colon
X\rightarrow Z^\bullet$ are proper mappings for all $ u \in \mathcal{U}$, and
$\emptyset \ne C\subset X$. Let $ A:=C\cap
\left(\bigcap_{u\in\mathcal{U}}G_u^{-1}(-S)\right)$ and $I_A : X \to Y^\bullet
$ be the indicator map defined by $I_A(x) = 0_Y $ if $x \in A$ and $I_A(x) = +
\infty_Y$ if $ x \not\in A$. It is well-known that the epigraph of the
conjugate mapping $(F+I_A)^\ast$, in general, is not a convex set. We show
that, however, it is "$k$-sectionally convex" in the sense that each section
form by the intersection of epi$(F+I_A)^\ast$ and any translation of a
"specific $k$-direction-subspace" is a convex subset, for any $k$ taking from
int$\,K$. The key results of the paper are the representations of the epigraph
of the conjugate mapping $(F+I_A)^\ast$ via the closure of the $k$-sectionally
convex hull of a union of epigraphs of conjugate mappings of mappings from a
family involving the data of the problem (RVP). The results are then given rise
to stable robust vector/convex vector Farkas lemmas which, in turn, are used to
establish new results on robust strong stable duality results for (RVP). It is
shown at the end of the paper that, when specifying the result to some concrete
classes of scalar robust problems (i.e., when $Y = \mathbb{R}$), our results
cover and extend several corresponding known ones in the literature.

28
The categories of this paper are: alg-geom
3
The categories of this paper are: physics
36
The categories of this paper are: cmp-lg
11
The categories of this paper are: hep-lat
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The categories of this paper are: acc-phys
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The categories of this paper are: solv-int
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The categories of this paper are: gr-qc
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The categories of this paper are: hep-th
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The categories of this paper are: hep-ex
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The categories of this paper are: math-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: ao-sci
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The categories of this paper are: plasm-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: nlin
1
The categories of this paper are: cs