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Lectures on nonsmooth optimization

Record Type:	Electronic resources : Monograph/item
Title/Author:	Lectures on nonsmooth optimizationby Qinian Jin.
Author:	Jin, Qinian.
Published:	Cham :Springer Nature Switzerland :2025.
Description:	xiii, 560 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
Subject:	Nonsmooth optimization.
Online resource:	https://doi.org/10.1007/978-3-031-91417-1
ISBN:	9783031914171$q(electronic bk.)

Lectures on nonsmooth optimization
Jin, Qinian.

Lectures on nonsmooth optimization[electronic resource] /by Qinian Jin. - Cham :Springer Nature Switzerland :2025. - xiii, 560 p. :ill., digital ;24 cm. - Texts in applied mathematics,v. 822196-9949 ;. - Texts in applied mathematics ;40..

Preface -- Introduction -- Convex sets and convex functions -- Subgradient and mirror descent methods -- Proximal algorithms -- Karush-Kuhn-Tucker theory and Lagrangian duality -- ADMM: alternating direction method of multipliers -- Primal dual splitting algorithms -- Error bound conditions and linear convergence -- Optimization with Kurdyka- Lojasiewicz property -- Semismooth Newton methods -- Stochastic algorithms -- References -- Index.

This book provides an in-depth exploration of nonsmooth optimization, covering foundational algorithms, theoretical insights, and a wide range of applications. Nonsmooth optimization, characterized by nondifferentiable objective functions or constraints, plays a crucial role across various fields, including machine learning, imaging, inverse problems, statistics, optimal control, and engineering. Its scope and relevance continue to expand, as many real-world problems are inherently nonsmooth or benefit significantly from nonsmooth regularization techniques. This book covers a variety of algorithms for solving nonsmooth optimization problems, which are foundational and recent. It first introduces basic facts on convex analysis and subdifferetial calculus, various algorithms are then discussed, including subgradient methods, mirror descent methods, proximal algorithms, alternating direction method of multipliers, primal dual splitting methods and semismooth Newton methods. Moreover, error bound conditions are discussed and the derivation of linear convergence is illustrated. A particular chapter is delved into first order methods for nonconvex optimization problems satisfying the Kurdyka-Lojasiewicz condition. The book also addresses the rapid evolution of stochastic algorithms for large-scale optimization. This book is written for a wide-ranging audience, including senior undergraduates, graduate students, researchers, and practitioners who are interested in gaining a comprehensive understanding of nonsmooth optimization.

ISBN: 9783031914171$q(electronic bk.)

Standard No.: 10.1007/978-3-031-91417-1doiSubjects--Topical Terms:

229311
Nonsmooth optimization.

LC Class. No.: QA402.5

Dewey Class. No.: 519.6

Lectures on nonsmooth optimization
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505 0 $a Preface -- Introduction -- Convex sets and convex functions -- Subgradient and mirror descent methods -- Proximal algorithms -- Karush-Kuhn-Tucker theory and Lagrangian duality -- ADMM: alternating direction method of multipliers -- Primal dual splitting algorithms -- Error bound conditions and linear convergence -- Optimization with Kurdyka- Lojasiewicz property -- Semismooth Newton methods -- Stochastic algorithms -- References -- Index.
520 $a This book provides an in-depth exploration of nonsmooth optimization, covering foundational algorithms, theoretical insights, and a wide range of applications. Nonsmooth optimization, characterized by nondifferentiable objective functions or constraints, plays a crucial role across various fields, including machine learning, imaging, inverse problems, statistics, optimal control, and engineering. Its scope and relevance continue to expand, as many real-world problems are inherently nonsmooth or benefit significantly from nonsmooth regularization techniques. This book covers a variety of algorithms for solving nonsmooth optimization problems, which are foundational and recent. It first introduces basic facts on convex analysis and subdifferetial calculus, various algorithms are then discussed, including subgradient methods, mirror descent methods, proximal algorithms, alternating direction method of multipliers, primal dual splitting methods and semismooth Newton methods. Moreover, error bound conditions are discussed and the derivation of linear convergence is illustrated. A particular chapter is delved into first order methods for nonconvex optimization problems satisfying the Kurdyka-Lojasiewicz condition. The book also addresses the rapid evolution of stochastic algorithms for large-scale optimization. This book is written for a wide-ranging audience, including senior undergraduates, graduate students, researchers, and practitioners who are interested in gaining a comprehensive understanding of nonsmooth optimization.
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