Constrained Optimization and Image Space Analysis: Volume 1: Separation of Sets and Optimality Conditions (Mathematical Concepts and Methods in Science and Engineering (49))

Over the last twenty years, Professor Franco Giannessi, a highly respected researcher, has been working on an approach to optimization theory based on image space analysis. His theory has been elaborated by many other researchers in a wealth of papers. Constrained Optimization and Image Space Analysis unites his results and presents optimization theory and variational inequalities in their light.

It presents a new approach to the theory of constrained extremum problems, including Mathematical Programming, Calculus of Variations and Optimal Control Problems. Such an approach unifies the several branches: Optimality Conditions, Duality, Penalizations, Vector Problems, Variational Inequalities and Complementarity Problems. The applications benefit from a unified theory.

From the reviews:

"This is a very substantial and useful monograph ... . it would be an excellent reference in a course at the graduate level in engineering or the advanced undergraduate level in mathematics, as well as for working mathematicians interested in optimization. This book is of unusually fine quality ... it will amply repay the time required. A notable feature of this work is the depth and completeness of coverage of many of the topics. ... Another aspect ... is the extensive use of examples." (Stephen M. Robinson, SIAM Review, Vol. 48 (2), 2006)