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.

Author Biography: Francisco J. Aragon (Ramon y Cajal Researcher), Miguel A. Goberna (Full Professor), Marco A. Lopez (Full Professor), and Margarita M. L. Rodriguez (Associate Professor) are members of the Optimization Laboratory at the University of Alicante. Marco A. Lopez is also Honorary Adjunct Professor of CIAO, Federation University, Ballarat (Australia). This group was created in the 1980s by the 2nd and 3rd 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. Lopez are co-authors of the books Linear Semi-Infinite Optimization (J. Wiley, 1998) and Post-Optimal Analysis in Linear Semi-Infinite Optimization (SpringerBrief, 2014).

1. Preliminaries.- Part I. Analytical Optimization.- 2. Convexity.- 3. Unconstrained Optimization.- 4. Convex Optimization.- Part II. Numerical Optimization.- 5. Unconstrained Optimization Algorithms.- 6. Constrained Optimization.- Solutions to selected exercises.- References.- Index.