Parametric condition numbers for optimization and complementarity problems
The concept of conditioning is central in numerical analysis. Given a specific numerical problem such as solving a system of linear or polynomial equations, a condition number is a measure of the sensitivity of the solution of a problem instance to changes in the input defining it. It is a fundamental tool in the analysis of the performance and numerical stability of algorithms. The long-term goal of this research plan is to create a flexible framework for condition numbers in optimization that incorporates specific characteristics of the problem of interest such as sparsity patterns as well as other structural properties in the input data.
This research project will develop new parametric condition numbers for various important problem classes including saddle-point problems, complementarity problems, and copositive programming. It will also use the new parametric condition numbers to analyze the performance of algorithms for these problem classes. Finally, it will establish connections between parametric condition numbers and robust optimization.
