Natural gas is an important source of energy that is regarded as essential for achieving the
politically set climate goals. In particular gas-fired power plants are valued as flexible
buffers to compensate for fluctuations in renewable electricity generation. Moreover gas
network operators face new challenges due to the liberalization of the European gas market.
Under the newly introduced entry-exit market regime gas network operators have to ensure that
all possible market outcomes can be transported over the network. Hence the operators of gas
networks require new aids for decision-making under uncertain conditions such as load
fluctuations or inaccuracies in physical parameters. To this end this thesis investigates a
general class of two-stage robust optimization problems using the example of gas network
operations under uncertainty. Three general solution methods are developed for this problem
class. The first two approaches use ideas from polynomial optimization to decide robust
feasibility or infeasibility. Both procedures consider polynomial formulations that are
approximated by semidefinite programs via the Lasserre relaxation hierarchy. The third approach
is based on a transformation of the two-stage robust problem into a number of single-stage
optimization problems. The resulting subproblems are approximated by mixed-integer linear
programs. By combining this method with additional preprocessing and aggregation steps it is
demonstrated that real-world problems can be solved efficiently within a short time.
