Foundations of Optimization [Hardcover]

This book covers the fundamental principles of optimization in finite dimensions. It develops the necessary material in multivariable calculus both with coordinates and coordinate-free, so recent developments such as semidefinite programming can be dealt with.

Differential Calculus.- Unconstrained Optimization.- Variational Principles.- Convex Analysis.- Structure of Convex Sets and Functions.- Separation of Convex Sets.- Convex Polyhedra.- Linear Programming.- Nonlinear Programming.- Structured Optimization Problems.- Duality Theory and Convex Programming.- Semi-infinite Programming.- Topics in Convexity.- Three Basic Optimization Algorithms.

From the reviews:

This book is an advanced graduate level text on the mathematical theory of optimization. & filled with many useful examples and counterexamples that provide intuition to support the more formal theorems and proofs. & There are also numerous exercises for the student. & The book will also be useful as a reference for researchers working in various areas of optimization. (Brian Borchers, The Mathematical Association of America, October, 2010)

G?lers book & is intended for postgraduates or researchers in optimization theory; however, it is also suitable as a textbook in a first-year graduate level course. The book covers a wide range of mathematical tools and results concerning the fundamental principles of optimization in finite-dimensional spaces. & this book can be a solid reference textbook, useful for graduate students in applied mathematics, economics, engineering, operations research, etc., and, more generally, for anyone wishing to learn the essential mathematical principles of optimization theory. (Giorgio Giorgi, Mathematical Reviews, Issue 2011 e)

...this textbook presents the state of the art in the theory of continuous optimization in a very transparent and accessible way. Several results are proved in two or more lóW