Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Inner approximation algorithm for solving linear multiobjective
  optimization problems   Benson's outer approximation algorithm and its variants are the most
frequently used methods for solving linear multiobjective optimization
problems. These algorithms have two intertwined components: one-dimensional
linear optimization one one hand, and a combinatorial part closely related to
vertex numeration on the other. Their separation provides a deeper insight into
Benson's algorithm, and points toward a dual approach. Two skeletal algorithms
are defined which focus on the combinatorial part. Using different
single-objective optimization problems - called oracle calls - yield different
algorithms, such as a sequential convex hull algorithm, another version of
Benson's algorithm with the theoretically best possible iteration count, the
dual algorithm of Ehrgott, L\"ohne and Shao, and the new algorithm. The new
algorithm has several advantages. First, the corresponding one-dimensional
optimization problem uses the original constraints without adding any extra
variables or constraints. Second, its iteration count meets the theoretically
best possible one. As a dual algorithm, it is sequential: in each iteration it
produces an extremal solution, thus can be aborted when a satisfactory solution
is found. The Pareto front can be "probed" or "scanned" from several directions
at any moment without adversely affecting the efficiency. Finally, it is well
suited to handle highly degenerate problems where there are many linear
dependencies among the constraints. On problems with ten or more objectives the
implementation shows a significant increase in efficiency compared to Bensolve
- due to the reduced number of iterations and the improved combinatorial
handling.

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The categories of this paper are: chem-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: ao-sci
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The categories of this paper are: atom-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: chao-dyn
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The categories of this paper are: cmp-lg
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The categories of this paper are: bayes-an
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The categories of this paper are: astro-ph
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The categories of this paper are: hep-th
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The categories of this paper are: funct-an
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The categories of this paper are: nlin
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The categories of this paper are: nucl-th
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The categories of this paper are: math-ph
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The categories of this paper are: adap-org
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The categories of this paper are: nucl-ex