In this work we study binary two-stage robust optimization problems with
objective uncertainty. We present an algorithm to calculate efficiently lower
bounds for the binary two-stage robust problem by solving alternately the
underlying deterministic problem and an adversarial problem. For the
deterministic problem any oracle can be used which returns an optimal solution
for every possible scenario. We show that the latter lower bound can be
implemented in a branch & bound procedure, where the branching is performed
only over the first-stage decision variables. All results even hold for
non-linear objective functions which are concave in the uncertain parameters.
As an alternative solution method we apply a column-and-constraint generation
algorithm to the binary two-stage robust problem with objective uncertainty.
We test both algorithms on benchmark instances of the uncapacitated
single-allocation hub-location problem and of the capital budgeting problem.
Our results show that the branch & bound procedure outperforms the
column-and-constraint generation algorithm.

本文研究具有目标不确定性的二阶段鲁棒优化问题，提出了一种算法，通过交替求解基础确定性问题和对抗性问题来高效计算二阶段鲁棒问题的下界。该算法适用于线性和非线性目标函数，研究发现其在非线性目标函数下，具有更高的性能表现。同时作者还测试了基于列生成和约束生成算法的另一种求解方法，发现分支定界算法的表现更胜一筹。