Algorithms for convex optimization /

"Convex optimization," as presented by Vishnoi (Yale Univ.), requires mastery of algorithms that find the minimal value of a convex function over a convex set. The goal of this book is to provide in-depth knowledge of such algorithms to readers in advanced undergraduate or introductory graduate classes. The book has five parts. The first two chapters form an introduction, offering historical and mathematical background. Chapters 3--5 introduce convexity and explain notions of efficiency. Chapters 6--8 discuss first-order methods, such as gradient descent. Chapters 9--11 focus on Newton's method. Finally, chapters 12 and 13 cover the ellipsoid method in linear programming and in convex optimization. The examples are chosen and presented in a way that bridges discrete and continuous optimization. Each chapter ends with a set of exercises. These do not come with solutions, though many come with a hint. Another useful addition at the end of each chapter is a "Notes" section that provides additional context for the covered material. Summing Up: Recommended. Upper-division undergraduates. Graduate students and faculty. --Miklos Bona, University of Florida