Lectures on Nonsmooth Optimization / by Qinian Jin.

Format:

Book

Author/Creator:

Jin, Qinian.

Series:

Texts in Applied Mathematics, 2196-9949 ; 82

Language:

English

Subjects (All):

Mathematical optimization.

Optimization.

Continuous Optimization.

Local Subjects:

Optimization.

Continuous Optimization.

Physical Description:

1 online resource (884 pages)

Edition:

1st ed. 2025.

Place of Publication:

Cham : Springer Nature Switzerland : Imprint: Springer, 2025.

Summary:

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.

Contents:

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.

Notes:

Description based on publisher supplied metadata and other sources.

Other Format:

Print version: Jin, Qinian Lectures on Nonsmooth Optimization

ISBN:

9783031914171

OCLC:

1527723843