This book, "Numerical Optimization: Theoretical and Practical Aspects" (Second Edition), is a comprehensive resource on numerical algorithms for optimization, covering both theoretical foundations and practical applications. Authored by J. Frédéric Bonnans, Claude Lemaréchal, J. Charles Gilbert, and Claudia A. Sagastizábal, the book is designed to familiarize readers with the behavior and practical use of optimization algorithms. It is intended for engineers, Master's and Ph.D. students, and researchers in applied mathematics and other disciplines where optimization is essential. The book is structured into four main parts: 1. **Unconstrained Problems**: Focuses on basic methods, line searches, Newtonian methods, conjugate gradient, and special methods. It includes a case study on seismic reflection tomography. 2. **Nonsmooth Optimization**: Introduces nonsmooth optimization, methods for nonsmooth functions, bundle methods, and applications in decomposition and constrained problems. 3. **Newton's Methods in Constrained Optimization**: Covers background, local methods for problems with equality constraints, and methods for problems with equality and inequality constraints. 4. **Interior-Point Algorithms for Linear and Quadratic Optimization**: Discusses linearly constrained optimization, predictor-corrector algorithms, non-feasible algorithms, self-duality, one-step methods, and Karmarkar's algorithm. The book emphasizes the practical value of optimization methods in solving real-world problems, while also providing a solid theoretical foundation. It includes numerous examples, computational exercises, and references to relevant software and resources. The authors have updated the content with new applications, theoretical discussions, and computational exercises to enhance understanding and practical skills.This book, "Numerical Optimization: Theoretical and Practical Aspects" (Second Edition), is a comprehensive resource on numerical algorithms for optimization, covering both theoretical foundations and practical applications. Authored by J. Frédéric Bonnans, Claude Lemaréchal, J. Charles Gilbert, and Claudia A. Sagastizábal, the book is designed to familiarize readers with the behavior and practical use of optimization algorithms. It is intended for engineers, Master's and Ph.D. students, and researchers in applied mathematics and other disciplines where optimization is essential. The book is structured into four main parts: 1. **Unconstrained Problems**: Focuses on basic methods, line searches, Newtonian methods, conjugate gradient, and special methods. It includes a case study on seismic reflection tomography. 2. **Nonsmooth Optimization**: Introduces nonsmooth optimization, methods for nonsmooth functions, bundle methods, and applications in decomposition and constrained problems. 3. **Newton's Methods in Constrained Optimization**: Covers background, local methods for problems with equality constraints, and methods for problems with equality and inequality constraints. 4. **Interior-Point Algorithms for Linear and Quadratic Optimization**: Discusses linearly constrained optimization, predictor-corrector algorithms, non-feasible algorithms, self-duality, one-step methods, and Karmarkar's algorithm. The book emphasizes the practical value of optimization methods in solving real-world problems, while also providing a solid theoretical foundation. It includes numerous examples, computational exercises, and references to relevant software and resources. The authors have updated the content with new applications, theoretical discussions, and computational exercises to enhance understanding and practical skills.