Worst case approach in convex minimization problems with uncertain data
Provides a quantitative framework for error analysis in convex optimization under data uncertainty, relevant for robust optimization practitioners.
The paper develops a worst-case error analysis for convex minimization with uncertain data, decomposing the error into two computable components to compare approximation and data uncertainty effects, demonstrated on a reaction-diffusion problem.
This paper concerns quantitative analysis of errors generated by incompletely known data in convex minimization problems. The problems are discussed in the mixed setting and the duality gap is used as the fundamental error measure. The influence of the indeterminate data is measured using the worst case scenario approach. The worst case error is decomposed into two computable quantities, which allows the quantitative comparison between errors resulting from the inaccuracy of the approximation and the data uncertainty. The proposed approach is demonstrated on a paradigm of a nonlinear reaction-diffusion problem together with numerical examples.