Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: New complexity results and algorithms for min-max-min robust
  combinatorial optimization   In this work we investigate the min-max-min robust optimization problem
applied to combinatorial problems with uncertain cost-vectors which are
contained in a convex uncertainty set. The idea of the approach is to calculate
a set of k feasible solutions which are worst-case optimal if in each possible
scenario the best of the k solutions would be implemented. It is known that the
min-max-min robust problem can be solved efficiently if k is at least the
dimension of the problem, while it is theoretically and computationally hard if
k is small. While both cases are well studied in the literature nothing is
known about the intermediate case, namely if k is smaller than but close to the
dimension of the problem. We approach this open question and show that for a
selection of combinatorial problems the min-max-min problem can be solved
exactly and approximately in polynomial time if some problem specific values
are fixed. Furthermore we approach a second open question and present the first
implementable algorithm with oracle-pseudopolynomial runtime for the case that
k is at least the dimension of the problem. The algorithm is based on a
projected subgradient method where the projection problem is solved by the
classical Frank-Wolfe algorithm. Additionally we derive a branch & bound method
to solve the min-max-min problem for arbitrary values of k and perform tests on
knapsack and shortest path instances. The experiments show that despite its
theoretical impact the projected subgradient method cannot compete with an
already existing method. On the other hand the performance of the branch &
bound method scales very well with the number of solutions. Thus we are able to
solve instances where k is above some small threshold very efficiently.

8
The categories of this paper are: hep-ex
16
The categories of this paper are: stat
26
The categories of this paper are: bayes-an
32
The categories of this paper are: atom-ph
25
The categories of this paper are: patt-sol
21
The categories of this paper are: adap-org
20
The categories of this paper are: acc-phys
23
The categories of this paper are: solv-int
37
The categories of this paper are: supr-con
6
The categories of this paper are: astro-ph
14
The categories of this paper are: math-ph
30
The categories of this paper are: q-alg
3
The categories of this paper are: physics
17
The categories of this paper are: q-fin
15
The categories of this paper are: nucl-ex
22
The categories of this paper are: chao-dyn