Nonlinear Optimization

Nonlinear Optimization provides a rigorous and comprehensive treatment of modern optimization methods, essential to applied mathematics and its numerous applications in engineering, economics, finance, statistics, and beyond. Designed with both graduate students and researchers in mind, the book builds on a solid mathematical foundation while presenting complex topics in an accessible and systematic way. In this volume, Andrzej Ruszczyński, an acknowledged expert in the field, meticulously integrates theory with practical methods through clear proofs, detailed illustrations, and numerous examples. The text covers key areas such as convex analysis, optimality conditions, duality theory, and numerical methods for solving unconstrained and constrained problems, offering a solid base for understanding both classical and contemporary issues. Drawing upon over a decade of refined lecture notes, Nonlinear Optimization also delves into advanced topics including strategies for nondifferentiable functions, semidefinite programming, metric regularity, stability of set-constrained systems, and sensitivity analysis. This comprehensive account equips readers with the tools to analyze new challenges, develop robust optimality theories, and fine-tune numerical solutions, making it an indispensable resource for anyone dedicated to the study of optimization.