Professors Kurdila and Zabarankin have done a great job putting together several topics of functional analysis, measure theory, convex analysis and optimization. However, although this book was prepared following the idea to provide the minimum of the theory required to understand the principle of functional analysis and convex analysis, I believe that this book is not easy for beginners (self-study).



If you have already studied functional analysis (using for instance chapters 1,2, 3 and 4 of kreyszig), introductory topology (using for instance chapter 2 of Gamelin and Greene) and measure theory (using for instance Bartle), I strongly believe that you will enjoy this book.



Chapter 1, 2 and 3 the authors introduce the basics of topology, functional analysis, and measure theory.



Chapter 4 is fantastic. They introduce differential calculus in vector spaces. They also provide several examples that make a connection between the notions of differentiability on these spaces and classical differentiability.



Chapter 5, 6 and 7 provide the main objective of the book which is optimization. One drawback of these chapters is that there are no examples. However, you can get several examples of control theory and calculus of variations for this chapter elsewhere such as in Optimization by Vector Space Methods by David G. Luenberger and Introduction to the Calculus of variations by Hans Sagan.



Finally, since the topics of this book were carefully chosen, this book seems to be a great choice to be used as text book in a PhD course of optimization for mathematicians, engineers, economists and physicists.

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