Explore a comprehensive lecture on nonmonotone operator splitting in nonlinear spaces, delivered by Russell Luke from the University of Goettingen. Delve into advanced optimization theory, algorithms, and applications as part of the Fields Institute's Optimization Lecture Series. Examine systems of linear inequalities, model categories, and concrete examples of underdetermined systems. Investigate convergence theory, numerical error, and the Conan Sphere Problem. Learn about prox mappings, set value maps, nonexpansiveness, and metric regularity. Discover applications in harmonic analysis and gain insights into linear convergence and selfmapping techniques. Enhance your understanding of structured feasibility problems and their solutions in nonlinear spaces.