Nonlinear Optimization

This textbook on nonlinear optimization focuses on model building, real world problems, and applications of optimization models to natural and social sciences. Organized into two parts, this book may be used as a primary text for courses on convex optimization and non-convex optimization. Definitions, proofs, and numerical methods are well illustrated and all chapters contain compelling exercises. The exercises emphasize fundamental theoretical results on optimality and duality theorems, numerical methods with or without constraints, and derivative-free optimization. Selected solutions are given. Applications to theoretical results and numerical methods are highlighted to help students comprehend methods and techniques.

• convexity
• coercivity
• linear regression
• Jensen's inequalities
• polynomial regression
• Lagrange duality
• Nelder and Mead method
• Fermat-Steiner problem
• Quasi-Newton methods
• optimization problems
• unconstrained optimization
• geometric optimizqtion
• quadratic optimiztion
• wolfe duality
• optimization algorithms
• line search methods
• gradient methods
• derivative-free optimization methods
• constrained optimization

“The book can be used for ‘upper-level undergraduate students of mathematics and statistics, and graduate students of industrial engineering.’ … I would recommend it to students for further reading and to colleagues for its nicely illustrated material that may be used for designing their lectures on nonlinear optimization.” (Martin Schmidt, SIAM Review, Vol. 62 (2), 2020)

“This book is a valuable contribution to optimization, its theory, methods and applications ... . Applications to theoretical results and numerical methods are highlighted to help readers, e.g., students, in order to understand and learn approaches and methods. This excellent book is clearly and well structured, analytically deep, well exemplified, beautifully illustrated, and written with care and taste.” (Gerhard-Wilhelm, WeberJoanna Majchrzak and Erik Kropat, zbMATH 1423.90001, 2019)

• Department of Mathematics, University of Alicante, Alicante, Spain

  Francisco J. Aragón, Miguel A. Goberna, Marco A. López, Margarita M.L. Rodríguez

Francisco J. Aragón (Ramón y Cajal Researcher), Miguel A. Goberna (Full Professor), Marco A. López (Full Professor), and Margarita M. L. Rodríguez (Associate Professor) are members of the Optimization Laboratory at the University of Alicante. Marco A. López is also Honorary Adjunct Professor of CIAO, Federation University, Ballarat (Australia). This group was created in the 1980s by the 2^nd and 3^rd authors, and works on the theory and methods for optimization problems. In particular, they have analyzed ordinary, semi-infinite, and infinite optimization problems from different perspectives (e.g., optimality, duality, stability, sensitivity and robustness), and have contributed with various numerical methods for linear and convex semi-infinite optimization problems and systems, together with new splitting algorithms for tackling feasibility and optimization problems.

Miguel A. Goberna and Marco A. López are co-authors of the books Linear Semi-Infinite Optimization (J. Wiley, 1998) and Post-Optimal Analysis in Linear Semi-Infinite Optimization (SpringerBrief, 2014).

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