Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: First-order algorithms for robust optimization problems via
  convex-concave saddle-point Lagrangian reformulation   Robust optimization (RO) is one of the key paradigms for solving optimization
problems affected by uncertainty. Two principal approaches for RO, the robust
counterpart method and the adversarial approach, potentially lead to
excessively large optimization problems. For that reason, first order
approaches, based on online-convex-optimization, have been proposed (Ben-Tal et
al. (2015), Kilinc-Karzan and Ho-Nguyen (2018)) as alternatives for the case of
large-scale problems. However, these methods are either stochastic in nature or
involve a binary search for the optimal value. We propose deterministic
first-order algorithms based on a saddle-point Lagrangian reformulation that
avoids both of these issues. Our approach recovers the other approaches'
O(1/epsilon^2) convergence rate in the general case, and offers an improved
O(1/epsilon) rate for problems with constraints which are affine both in the
decision and in the uncertainty. Experiment involving robust quadratic
optimization demonstrates the numerical benefits of our approach.

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The categories of this paper are: cond-mat
1
The categories of this paper are: cs
6
The categories of this paper are: astro-ph
22
The categories of this paper are: chao-dyn
33
The categories of this paper are: plasm-ph
32
The categories of this paper are: atom-ph
37
The categories of this paper are: supr-con
11
The categories of this paper are: hep-lat
26
The categories of this paper are: bayes-an
20
The categories of this paper are: acc-phys
9
The categories of this paper are: nlin
27
The categories of this paper are: comp-gas
15
The categories of this paper are: nucl-ex
24
The categories of this paper are: dg-ga
14
The categories of this paper are: math-ph
3
The categories of this paper are: physics