Numerical minimization of an objective function is analyzed in this book to understand solution
algorithms for optimization problems. Multiset-mappings are introduced to engineer numerical
minimization as a repeated application of an iteration mapping. Ideas from numerical
variational analysis are extended to define and explore notions of continuity and
differentiability of multiset-mappings and prove a fixed-point theorem for iteration mappings.
Concepts from dynamical systems are utilized to develop notions of basin size and basin
entropy. Simulations to estimate basins of attraction to measure and classify basin size and
to compute basin are included to shed new light on convergence behavior in numerical
minimization. Graduate students researchers and practitioners in optimization and mathematics
who work theoretically to develop solution algorithms will find this book a useful resource.
