This textbook examines a broad range of problems in science and engineering, describing key numerical methods applied to real life. The case studies presented are in such areas as data fitting, vehicle route planning and optimal control, scheduling and resource allocation, sensitivity calculations and worst-case analysis.

Among the main topics covered:

- one-variable optimization — optimality conditions, direct search and gradient
- unconstrained optimization in n variables — solution methods including Nelder and Mead simplex, steepest descent, Newton, Gauss–Newton, and quasi-Newton techniques, trust regions and conjugate gradients.
- constrained optimization in n variables — solution methods including reduced-gradients, penalty and barrier methods, sequential quadratic programming, and interior point techniques
- an introduction to global optimization
- an introduction to automatic differentiation

Chapters are self-contained with exercises provided at the end of most sections. Nonlinear Optimization with Engineering Applications is ideal for self-study and classroom use in engineering courses at the senior undergraduate or graduate level. The book will also appeal to postdocs and advanced researchers interested in the development and use of optimization algorithms.