Best Reference Books – Convex Optimization

We have compiled the list of Top 10 Best Reference Books on Convex Optimization subject. These books are used by students of top universities, institutes and colleges. Here is the full list of top 10 best books on Convex Optimization along with reviews.

Kindly note that we have put a lot of effort into researching the best books on Convex Optimization subject and came out with a recommended list of top 10 best books. The table below contains the Name of these best books, their authors, publishers and an unbiased review of books on "Convex Optimization" as well as links to the Amazon website to directly purchase these books. As an Amazon Associate, we earn from qualifying purchases, but this does not impact our reviews, comparisons, and listing of these top books; the table serves as a ready reckoner list of these best books.

1. “Convex Optimization Theory” by Dimitri P Bertsekas

“Convex Optimization Theory” Book Review: The book covers the basic theory of convex sets and functions in finite dimensions. It offers the analytical/geometrical foundations of convex optimization and duality theory. The book introduces convexity theory to the readers. It also provides analysis of transparent geometrical lines to develop the fundamental duality between descriptions of convex sets and functions in terms of points and in terms of hyperplanes. The book highlights convexity theory and abstract duality which are applied to problems of constrained optimization. Fenchel and conic duality, and game theory are thoroughly explained to develop the sharpest possible duality results within a highly visual geometric framework.

2. “Convex Optimization” by Stephen Boyd, Lieven Vandenberghe

“Convex Optimization” Book Review: The book serves as a primary textbook for convex optimization with engineering applications or as an alternate text for a more traditional course on linear or nonlinear optimization. It gives a comprehensive introduction to the tools, techniques and applications of convex optimization. It covers Convex optimization problems that arise frequently in many different fields. The book focuses on recognizing convex optimization problems and then finding the most appropriate technique for solving them. Numerous worked examples and homework exercises are included in the book that will appeal to students, researchers and practitioners in fields such as engineering, computer science, mathematics, statistics, finance, and economics.

3. “Combinatorial Optimization: Algorithms and Complexity (Dover Books on Computer Science)” by Christos H Papadimitriou and Kenneth Steiglitz

“Combinatorial Optimization Algorithms and Complexity (Dover Books on Computer Science)” Book Review: The book is designed for graduate-level students with backgrounds in computer science, operations research, and electrical engineering. It includes a novel algorithmic exposition of the simplex method. It also provides a discussion on the Soviet ellipsoid algorithm for linear programming. The book features efficient algorithms for network flow, matching, spanning trees, and matroids. Each chapter contains problems for readers to evaluate themselves. The book also includes the theory of NP-complete problems, approximation algorithms and local search heuristics for NP-complete problems.

4. “Lectures On Convex Sets” by Valeriu Soltan

“Lectures On Convex Sets” Book Review: This book is a useful guide to researchers in convex geometry. It can also be referred to by graduate students and even ambitious undergraduates in mathematics, optimization, and operations research. The book covers the fundamentals of the algebraic and topological properties of convex sets in great depth. It provides a systematic treatment of algebraic and topological properties of convex sets (possibly non closed or unbounded) in the n dimensional Euclidean space. It contains chapters such as general properties of convex sets and convex hulls, cones and conic hulls, polyhedral sets, the extreme structure, support and separation properties of convex sets. The exercises included in the book helps the readers to understand the concept in an easier way.

5. “Lagrange-type Functions in Constrained Non-Convex Optimization (Applied Optimization)” by Alexander M Rubinov and Xiao-qi Yang

“Lagrange-type Functions in Constrained Non-Convex Optimization (Applied Optimization)” Book Review: The book offers a powerful approach, both as a theoretical tool and a computational vehicle, for the study of constrained optimization problems. The book gives a systematic and unified presentation of many important results that have been obtained in this area during the last several years. It develops a unified approach to duality and penalization and to convergence analysis of the first and second order optimality conditions. The book teaches how to generalize classical Lagrange and penalty functions, in order to obtain an appropriate scheme for reducing constrained optimization problems to unconstrained ones that will be suitable for sufficiently broad classes of optimization problems from both the theoretical and computational viewpoints.

6. “Convex Optimization in Normed Spaces: Theory, Methods and Examples (SpringerBriefs in Optimization)” by Juan Peypouquet

Convex Optimization in Normed Spaces Theory, Methods and Examples (SpringerBriefs in Optimization)” Book Review: This book is an ideal guide for graduate students and researchers who wish to get acquainted with the main theoretical and practical tools for the numerical minimization of convex functions on Hilbert spaces. The book covers all the concepts about convex optimization. It contains the main tools that are necessary to conduct independent research on the topic. The book may be useful for any researcher working on related fields, as well as teachers giving graduate-level courses on the topic. The book contains chapters such as basic functional analysis along with Convex Analysis and Subdifferential Calculus.

7. “Introductory Lectures on Convex Optimization: A Basic Course (Applied Optimization)” by Yurii Nesterov
8. “Selected Applications of Convex Optimization (Springer Optimization and Its Applications)” by Li Li

“Selected Applications of Convex Optimization (Springer Optimization and Its Applications)” Book Review: The book emphasizes on the applications of convex optimization. It gives a thorough knowledge on support vector machines, parameter estimation, norm approximation and regularization and semi-definite programming problems. It also contains convex relaxation, and geometric problems.The book offers concrete guidance, helping readers recognize and formulate convex optimization problems they might encounter in practice. It also derivations in depth for a better understanding. The book also offers exercises at the end of each chapter.

9. “Conjugate Duality in Convex Optimization (Lecture Notes in Economics and Mathematical Systems)” by Radu Ioan Bot

“Conjugate Duality in Convex Optimization (Lecture Notes in Economics and Mathematical Systems)” Book Review: This book presents new achievements and results in the theory of conjugate duality for convex optimization problems. It emphasize its strong connections with different topics in convex analysis, nonlinear analysis, functional analysis and in the theory of monotone operators. It provides the readers with the knowledge of perturbation approach as a fundamental tool for developing the so-called conjugate duality t- ory. The reader also receives deep insights into biconjugate calculus for convex functions and the relations between different existing strong duality notions. The book offers thorough explanation on several unconventional Fenchel duality topics. It also covers the applications of the convex duality theory in the field of monotone operators.

10. “Convex Optimization Algorithms” by Dmitri P. Bertsekas

“Convex Optimization Algorithms” Book Review: The book provides an accessible, concise, and intuitive presentation of algorithms for solving convex optimization problems. It aims at an intuitive exposition that makes use of visualization where possible. It gives the readers a knowledge of the theory of descent and approximation methods, including gradient and subgradient projection methods, cutting plane and simplicial decomposition methods, and proximal methods. It also helps them Develops the modern theory of coordinate descent methods, including distributed asynchronous convergence analysis. The book Includes optimal algorithms based on extrapolation techniques and associated rate of convergence analysis. It also contains numerous examples and illustrations as well as exercise questions.

People who are searching for Free downloads of books and free pdf copies of these top 10 books on Convex Optimization – we would like to mention that we don’t have free downloadable pdf copies of these good books and one should look for free pdf copies from these Authors only if they have explicitly made it free to download and read them.

We have created a collection of best reference books on "Convex Optimization" so that one can readily see the list of top books on "Convex Optimization" and buy the books either online or offline.

If any more book needs to be added to the list of best books on Convex Optimization subject, please let us know.

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