Proof Mining in Convex Optimization
In this Project we aim at using proof-theoretic methods from logic for the extraction of new data (such as effective bounds, “proof mining”) from prima facie noneffective proofs in convex optimization and related areas. We need to tailor the proof-theoretic methods to the specific domain of applications and will then apply them for the extraction of rates of asymptotic regularity, metastability (in the sense of T. Tao) and convergence of central iterative procedures used in convex optimization. In particular, we will study convergence proofs which make use of facts from the abstract theory of set-valued operators (e.g. maximally monotone operators).
(DFG 04/2018, Kohlenbach)