Lectures on Convex Optimization (Springer Optimization and Its Applications, 137)

Convex optimization problems form probably the only class of optimization problems for which global optimal solution can be found with the help of a reasonable computational effort. More precisely, one should consider a required computational effort as a function of the size and the structure of the problem. While not all convex optimization problems can be solved in the sense described above ( e.g. , so-called copositive programming), and some nonconvex problems can be reduced to solvable convex ones by clever nonlinear transformations (e.g. , so-called geometric programming), the class of convex optimization problems is undoubtedly the most important class of optimization problems for which finding the global optimal solution is plausible.The book under review provides a comprehensive introduction to the exciting area of convex optimization. Starting with basic algorithms, the author quickly moves to the frontiers of the research including structural and algorithmic nonsmooth optimization, global analysis of the regularized Newton method and optimization in relative scale. The author, who is one of the leading researchers in the field, greatly contributed to structural optimization (interior-point methods ), nonsmooth optimization (smoothing technique) and acceleration technique for many classical algorithms.The book is clearly written and provides all necessary theoretical (duality theory , optimality conditions , complexity estimates) and algorithmic foundations of convex optimization. It is accessible for an undergraduate student (mathematics, engineering , computer science, economics) without any preliminary background in optimization , who is prepared to put a corresponding effort in learning the material. But even experts in optimization theory will find a lot of exciting material available only in research papers.Perhaps one area which is beyond the scope of the book is stochastic optimization which became especially important in connection with recent developments in machine learning and big data analysis. But the reader who mastered the material of the book will be well equipped for studying research papers in this area.In my estimate this is one of the best (if not the best!) books in the area of convex optimization published recently by the true leader in the field.

I am in the middle of a masters program in data analytics. Of all the textbooks I bought, this one does the best job at fully explaining concepts including the underlying math. This compares to other textbooks which make alot of assumptions about prior knowledge in ways that leave it unclear how to fill in the missing gaps.

This book is extremely theoretical and it is a colection of theoretical results.Explanations are very limited and no example in the book! The book has a value of zero if you want to learn thesubject yourself.