Numerical Optimization: Theoretical and Practical Aspects, Second Edition by J. Frédéric Bonnans, J. Charles Gilbert, Claude Lemaréchal, and Claudia A. Sagastizábal is a comprehensive book on numerical algorithms for optimization, their theoretical foundations, convergence properties, implementation, and practical applications. The book is aimed at engineers, graduate students, and researchers in applied mathematics and other disciplines where optimization is needed. It covers a wide range of optimization problems, including unconstrained optimization, nonsmooth optimization, and constrained optimization, with a focus on practical aspects and real-world applications. The book is divided into four parts. The first part covers algorithms for unconstrained optimization, including basic methods, line-searches, Newtonian methods, conjugate gradient methods, and special methods. The second part discusses nonsmooth optimization, including an introduction to nonsmooth optimization, some methods in nonsmooth optimization, bundle methods, and applications of nonsmooth optimization. The third part focuses on Newton's methods in constrained optimization, including background, local methods for problems with equality constraints, local methods for problems with equality and inequality constraints, exact penalization, and globalization by line-search. The fourth part presents interior-point algorithms for linear and quadratic optimization, including linearly constrained optimization and simplex algorithm, linear monotone complementarity, predictor-corrector algorithms, non-feasible algorithms, self-duality, one-step methods, and complexity of linear optimization problems with integer data. The book includes a detailed introduction to optimization, an overview of optimization theory, and a discussion of the practical value of optimization methods. It also provides a detailed discussion of the theoretical properties of optimization methods, including convergence properties, global and local convergence, and the efficiency of algorithms in solving real-world problems. The book also includes a variety of computational exercises and examples, as well as a detailed discussion of existing software for nonlinear optimization. The book is written in English and is intended for a broad audience of researchers and practitioners in optimization.Numerical Optimization: Theoretical and Practical Aspects, Second Edition by J. Frédéric Bonnans, J. Charles Gilbert, Claude Lemaréchal, and Claudia A. Sagastizábal is a comprehensive book on numerical algorithms for optimization, their theoretical foundations, convergence properties, implementation, and practical applications. The book is aimed at engineers, graduate students, and researchers in applied mathematics and other disciplines where optimization is needed. It covers a wide range of optimization problems, including unconstrained optimization, nonsmooth optimization, and constrained optimization, with a focus on practical aspects and real-world applications. The book is divided into four parts. The first part covers algorithms for unconstrained optimization, including basic methods, line-searches, Newtonian methods, conjugate gradient methods, and special methods. The second part discusses nonsmooth optimization, including an introduction to nonsmooth optimization, some methods in nonsmooth optimization, bundle methods, and applications of nonsmooth optimization. The third part focuses on Newton's methods in constrained optimization, including background, local methods for problems with equality constraints, local methods for problems with equality and inequality constraints, exact penalization, and globalization by line-search. The fourth part presents interior-point algorithms for linear and quadratic optimization, including linearly constrained optimization and simplex algorithm, linear monotone complementarity, predictor-corrector algorithms, non-feasible algorithms, self-duality, one-step methods, and complexity of linear optimization problems with integer data. The book includes a detailed introduction to optimization, an overview of optimization theory, and a discussion of the practical value of optimization methods. It also provides a detailed discussion of the theoretical properties of optimization methods, including convergence properties, global and local convergence, and the efficiency of algorithms in solving real-world problems. The book also includes a variety of computational exercises and examples, as well as a detailed discussion of existing software for nonlinear optimization. The book is written in English and is intended for a broad audience of researchers and practitioners in optimization.