Introduction to Nonlinear and Global Optimization

This text provides a compelling introduction to global and nonlinear optimization, providing both students of mathematics and interdisciplinary sciences with a strong background to continue their studies in these fields. The book offers insights into relevant concepts through numerous useful numerical examples and exercises.

Nonlinear Optimization is an intriguing area of study where mathematical theory, algorithms and applications converge to calculate the optimal values of continuous functions. Within this subject, Global Optimization aims at finding global optima for difficult problems in which many local optima might exist.

This book provides a compelling introduction to global and non-linear optimization providing interdisciplinary readers with a strong background to continue their studies into these and other related fields. The book offers insight in relevant concepts such as "region of attraction" and "Branch-and-Bound" by elaborating small numerical examples and exercises for the reader to follow.

Can serve as both a graduate and undergraduate text in courses focusing on numerical optimization methods Focuses on problems relating to "region of attraction" and "branch and bound" Contains several instructional numerical examples and excercises providing the reader with working knowledge of the material

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This self-contained text provides a solid introduction to global and nonlinear optimization, providing students of mathematics and interdisciplinary sciences with a strong foundation in applied optimization techniques. The book offers a unique hands-on and critical approach to applied optimization which includes the presentation of numerous algorithms, examples, and illustrations, designed to improve the reader's intuition and develop the analytical skills needed to identify optimization problems, classify the structure of a model, and determine whether a solution fulfills optimality conditions.

Key features of "Introduction to Nonlinear and Global Optimization":

• Offers insights into relevant concepts such as "regions of attraction", "branch-and-bound", and "cross-cutting" methods as well as many other useful methodologies.

-Exhibits numerical examples and exercises developing the reader's familiarity with the terminology and algorithms that are frequently encountered in scientific literature.

• Presents various heuristic and stochastic optimization techniques demonstrating how each be applied to a variety of models from biology, engineering, finance, chemistry, and economics.

This book is intended to serve as a primary text in an advanced undergraduate or graduate course focusing on nonlinear and global optimization and requires an understanding of basic calculus and linear algebra.

Contenu
Mathematical modeling, cases.- NLP optimality conditions.- Goodness of optimization algorithms.- Nonlinear Programming algorithms.- Deterministic GO algorithms.- Stochastic GO algorithms.