Foundations of Optimization (eBook)

The book gives a detailed and rigorous treatment of the theory of
optimization (unconstrained optimization, nonlinear programming,
semi-infinite programming, etc.) in finite-dimensional spaces.
The fundamental results of convexity theory and the theory of duality in
nonlinear programming and the theories of linear inequalities, convex
polyhedra, and linear programming are covered in detail. Over two
hundred, carefully selected exercises should help the students master
the material of the book and give further insight. Some of the most
basic results are proved in several independent ways in order to give
flexibility to the instructor. A separate chapter gives extensive
treatments of three of the most basic optimization algorithms (the
steepest-descent method, Newton's method, the conjugate-gradient
method). The first chapter of the book introduces the necessary
differential calculus tools used in the book. Several chapters contain
more advanced topics in optimization such as Ekeland's
epsilon-variational principle, a deep and detailed study of separation
properties of two or more convex sets in general vector spaces, Helly's
theorem and its applications to optimization, etc. The book is suitable
as a textbook for a first or second course in optimization at the
graduate level. It is also suitable for self-study or as a reference
book for advanced readers. The book grew out of author's experience in
teaching a graduate level one-semester course a dozen times since 1993.
Osman Guler is a Professor in the Department of Mathematics and
Statistics at University of Maryland, Baltimore County. His research
interests include mathematical programming, convex analysis, complexity
of optimization problems, and operations research.