Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An exact dynamic programming algorithm, lower and upper bounds, applied
  to the large block sale problem   In this article, we address a class of non convex, integer, non linear
mathematical programs using dynamic programming. The mathematical program
considered, whose properties are studied in this article, may be used to model
the optimal liquidation problem of a single asset portfolio, held in a very
large quantity, in a low volatility and perfect memory market, with few market
participants. In this context, the Portfolio Manager's selling actions convey
information to market participants, which in turn lower bid prices and further
penalize the liquidation proceeds we attempt to maximize. We show the problem
can be solved exactly using Dynamic Programming (DP) in polynomial time.
However, exact resolution is only efficient for small instances. For medium
size and large instances, we introduce dedicated heuristics which provide thin
admissible solutions, hence tight lower bounds for the initial problem. We also
benchmark them against a commercial solver, such as LocalSolver [7]. We are
also interested in the continuously relaxed problem, which is non convex.
Firstly, we use continuous solutions, obtained by free solver NLopt [26] and
transform them into thin admissible solutions of the discrete problem.
Secondly, we provide, under some convexity assumptions, an upper bound for the
continuous relaxation, and hence for the initial (integer) problem. Numerical
experiments confirm the quality of proposed heuristics (lower bounds), which
often reach the optimal, or prove very tight, for small and medium size
instances, with a very fast CPU time. Our upper bound, however, is not tight.

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The categories of this paper are: plasm-ph
2
The categories of this paper are: math
4
The categories of this paper are: cond-mat
0
The categories of this paper are: hep-ph
13
The categories of this paper are: quant-ph
20
The categories of this paper are: acc-phys
29
The categories of this paper are: funct-an
5
The categories of this paper are: gr-qc
8
The categories of this paper are: hep-ex
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The categories of this paper are: q-alg
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The categories of this paper are: stat
25
The categories of this paper are: patt-sol
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The categories of this paper are: ao-sci
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The categories of this paper are: hep-lat
6
The categories of this paper are: astro-ph
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The categories of this paper are: nlin