Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An outer approximation algorithm for multi-objective mixed-integer
  linear and non-linear programming   In this paper, we present the first outer approximation algorithm for
multi-objective mixed-integer linear programming problems with any number of
objectives. The algorithm also works for certain classes of non-linear
programming problems. It produces the non-dominated extreme points as well as
the facets of the convex hull of these points. The algorithm relies on an
oracle which solves single-objective weighted-sum problems and we show that the
required number of oracle calls is polynomial in the number of facets of the
convex hull of the non-dominated extreme points in the case of multiobjective
mixed-integer programming (MOMILP). Thus, for MOMILP problems for which the
weighted-sum problem is solvable in polynomial time, the facets can be computed
with incremental-polynomial delay. From a practical perspective, the algorithm
starts from a valid lower bound set for the non-dominated extreme points and
iteratively improves it. Therefore it can be used in multi-objective
branch-and-bound algorithms and still provide a valid bound set at any stage,
even if interrupted before converging. Moreover, the oracle produces Pareto
optimal solutions, which makes the algorithm also attractive from the primal
side in a multi-objective branch-and-bound context. Finally, the oracle can
also be called with any relaxation of the primal problem, and the obtained
points and facets still provide a valid lower bound set. A computational study
on a set of benchmark instances from the literature and new non-linear
multi-objective instances is provided.

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The categories of this paper are: hep-th
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The categories of this paper are: chem-ph
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The categories of this paper are: stat
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The categories of this paper are: physics
33
The categories of this paper are: plasm-ph
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The categories of this paper are: q-fin
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The categories of this paper are: bayes-an
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The categories of this paper are: cs
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The categories of this paper are: hep-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: nucl-th
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The categories of this paper are: atom-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: cond-mat
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The categories of this paper are: supr-con
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The categories of this paper are: adap-org