Lectures on Convex Optimization is devoted to well structured and efficiently solvable convex optimization problems, with an emphasis on conic quadratic and semidefinite programming. The authors begin with linear programming, and then progress to conic programming. [I really enjoyed their description of the transition from linear to general conic programming!]. They then discuss two special conic optimization problems namely second order cone programming, and semidefinite programming. Numerous applications of conic programming espcially in filter design, Lyapunov stability analysis, and structural design are presented. The book concludes with a discussion on the computational tractability of convex programs, and primal dual interior point algorithms to solving general conic optimization problems.
One can then take on the likes of Renegar's recent book on interior point methods, and Nesterov and Nemirovski's seminal treatise on the general theory of interior point methods in convex optimization, at a more advanced level.
My only minor comments are :- (a) The organization of the book as a series of 6 lectures is misleading, since there is quite a lot of material covered in each lecture. (b) The book has a very short [almost nonexistent] bibliography.
All in all, a good workout and an encyclopedic source for anyone interested in theory and applications of convex optimization. Highly recommended!.