Dry book!Large -scale convex optimization based on monotonous operator

Source: Specialty

This article is a book, it is recommended to read for 5 minutes

This book provides a strong and higher -level insight for the first -order convex optimization method.

We wrote this book to share an elegant perspective, which provides a strong and higher -level insight for the first -order convex optimization method. The first -order convex optimization method more effectively solved the problem of large -scale optimization issues began in the 1960s and 1970s, but the focus of the field at that time was the second -order method, and the latter more effectively solved smaller problems. At the beginning of the 21st century, with the improvement of computing power and the availability of big data, the first -order optimization method became mainstream. In this modern era, the author entered the field of optimization and found that (but no invention) above, and we hope to share it through this book.

https://laarge-scale-book.mathopt.com/

Our goal is to uniformly analyze the convex optimization algorithm through the abstraction of monotonists.

This book is prepared for mathematicians and engineers. We are elegant by showing abstraction and challenging (interesting) in some aspects to attract mathematicians. We call on engineers, optimization of users, and the diversity of simple technology and algorithms. In some examples, we have encountered engineers who only know the gradient decrease and ADMM. Although they are very powerful, they are not generally feasible or best. This book enable readers to choose or even design the separation method that is most suitable for any given problems. The background requirements of the reader are a good understanding of the basic concepts of high -level calculus, linear algebra, basic probability, and the basic concept of convex analysis. These knowledge involves the convex sets of Boyd and VANDENBERGHE. Functions, convex optimization problems and convex pairs. (Mathematics) The background of the probability theory of analysis and measurement theory is helpful, but it is not necessary. Informal, this book presets interest in convex optimization and appreciate it as a useful tool. In order to make the discussion concise, we focus on the optimization algorithm rather than the engineering and scientific origin of the optimization problem solved by the discussion algorithm.

Annotment

INTRODUCTION and Preliminaries

Monotone Operators and Base Splitting Schemes

Set-valued Operators

Monotone Operators

NoneXPANSIVE and AND ADRAGED Operators, FIXED-POINT ITERATION

Resolvent

Proximal Point Method, Operator Splitting

Variable Metric Methods

Primal-Dual Methods

Infimal PostComposition Technique

Dualization technique

Variable Metric Technique

Gaussian Elimination Technology

Linearization technique

Parallel Computing

Stochastic Coordine Update Methods

Asynchronous Coordinal Update Methods

Stochastic optimization

Admm-type method

Flip-Admm

Derived Admm-Type Methods

Duality in Splitting Methods

Maximality and Monotone Operator theory

Distitd and Decentralized Optimization

Acceleration

Scaled relative graphs

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