Giorgi G. Mathematics of Optimization. Smooth and Nonsmooth Case 2004

Textbook in PDF format

The book is intended for people (graduates, researchers, but also undergraduates with a good mathematical background) involved in the study of (static) optimization problems (in finite-dimensional spaces). It contains a lot of material, from basic tools of convex analysis to optimality conditions for smooth optimization problems, for non smooth optimization problems and for vector optimization problems.
The development of the subjects are self-contained and the bibliographical references are usually treated in different books (only a few books on optimization theory deal also with vector problems), so the book can be a starting point for further readings in a more specialized literature.
Assuming only a good (even if not advanced) knowledge of mathematical analysis and linear algebra, this book presents various aspects of the mathematical theory in optimization problems. The treatment is performed in finite-dimensional spaces and with no regard to algorithmic questions. After two chapters concerning, respectively, introductory subjects and basic tools and concepts of convex analysis, the book treats extensively mathematical programming problems in the smmoth case, in the nonsmooth case and finally vector optimization problems.
Self-contained
Clear style and results are either proved or stated precisely with adequate references
The authors have several years experience in this field
Several subjects (some of them non usual in books of this kind) in one single book, including nonsmooth optimization and vector optimization problems
Useful long references list at the end of each chapter
Convex Sets, Convex and Generalized Convex Functions
Smooth Optimization Problems. Saddle Point Conditions
Nonsmooth Optimization Problems
Duality
Vector Optimization
Subject Index