Logical Analysis of Proofs in Non-Smooth Optimization Using Set-Valued Monotone Operators

Explore the logical foundations of non-smooth optimization through set-valued monotone operator theory in this conference lecture delivered at the Erwin Schrödinger International Institute for Mathematics and Physics. Delve into advanced mathematical analysis techniques that examine proof structures in optimization problems where traditional smooth analysis methods fail to apply. Learn how logical methods can be systematically applied to understand and analyze proofs involving set-valued monotone operators, which are fundamental tools in convex analysis and optimization theory. Discover the intersection of mathematical logic, proof theory, and optimization mathematics as part of the broader reverse mathematics paradigm that seeks to determine the minimal axioms needed for mathematical theorems. Gain insights into how proof-theoretic methods can extract computational information from existence proofs in non-smooth optimization settings, contributing to both theoretical understanding and practical algorithmic development in optimization theory.