Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Geometrical Analysis of a Class of Nonconvex Conic Programs for Convex
  Conic Reformulations of Quadratic and Polynomial Optimization Problems   We present a geometrical analysis on the completely positive programming
reformulation of quadratic optimization problems and its extension to
polynomial optimization problems with a class of geometrically defined
nonconvex conic programs and their covexification. The class of nonconvex conic
programs is described with a linear objective functionin a linear space $V$,
and the constraint set is represented geometrically as the intersection of a
nonconvex cone $K \subset V$, a face $J$ of the convex hull of $K$ and a
parallel translation $L$ of a supporting hyperplane of the nonconvex cone $K$.
We show that under a moderate assumption, the original nonconvex conic program
can equivalently be reformulated as a convex conic program by replacing the
constraint set with the intersection of $J$ and the hyperplane $L$. The
replacement procedure is applied to derive the completely positive programming
reformulation of quadratic optimization problems and its extension to
polynomial optimization problems.

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The categories of this paper are: hep-ex
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The categories of this paper are: q-bio
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The categories of this paper are: math-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: atom-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-th
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The categories of this paper are: solv-int
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The categories of this paper are: cs
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The categories of this paper are: hep-lat
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The categories of this paper are: eess
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The categories of this paper are: quant-ph
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The categories of this paper are: physics
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The categories of this paper are: mtrl-th
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The categories of this paper are: nucl-th
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The categories of this paper are: comp-gas