Recent Progress in Proof Mining in Nonlinear Analysis

During the last two decades the program of ‘proof mining’ emerged which uses tools from mathematical logic (so-called proof interpretations) to systematically extract explicit quantitative information (e.g. rates of convergence) from prima facie nonconstructive proofs (e.g. convergence proofs). This has been applied particularly successful in the context of nonlinear analysis: fixed point theory, ergodic theory, topological dynamics, convex optimization and abstract Cauchy problems. In this paper we give a survey on some of the results, both on the logical foundation of proof mining as well as its applications in nonlinear analysis, obtained since the monograph [65] appeared.