Generalized convexity and optimization. Theory and applications.

*(English)*Zbl 1157.49001
Lecture Notes in Economics and Mathematical Systems 616. Berlin: Springer (ISBN 978-3-540-70875-9/pbk). xiv, 246 p. (2009).

The optimization of generalized convex functions plays an important role in many applications, especially in economics. The book gives an introduction to the theory and the application of such functions and their use in optimization. After a review of classical convex analysis the book presents concepts of generalized convexity for non-differentiable and differentiable functions. Further topics of the book are the role of generalized convexity in optimization, the relationship with concepts of generalized monotonicity, specialized results for quadratic and fractional functions, and sequential methods for generalized convex fractional programs. The book is self-contained and includes many exercises with solutions. I highly recommend this book to researchers and graduate students interested in optimization and their applications.

Reviewer: Walter Alt (Jena)