First-Order Methods in Optimization

丛 书 名：Volume 25 of MOS-SIAM Series on Optimization

作     者：Amir Beck 

I S B N：(纸本) 9781611974980 

出 版 社：SIAM-Society for Industrial and Applied Mathematics 

出 版 年：2017年

主 题 词：nonlinear optimization convex analysis first order methods decomposition methods scientific computing 

学科分类：12[管理学] 1201[管理学-管理科学与工程(可授管理学、工学学位)] 07[理学] 070105[理学-运筹学与控制论] 0701[理学-数学] 

摘      要：The primary goal of this book is to provide a self-contained, comprehensive study of the main first-order methods that are frequently used in solving large-scale problems. First-order methods exploit information on values and gradients/subgradients (but not Hessians) of the functions composing the model under consideration. With the increase in the number of applications that can be modeled as large or even huge-scale optimization problems, there has been a revived interest in using simple methods that require low iteration cost as well as low memory *** author has gathered, reorganized, and synthesized (in a unified manner) many results that are currently scattered throughout the literature, many of which cannot be typically found in optimization ***-Order Methods in Optimization offers comprehensive study of first-order methods with the theoretical foundations; provides plentiful examples and illustrations; emphasizes rates of convergence and complexity analysis of the main first-order methods used to solve large-scale problems; and covers both variables and functional decomposition ***: This book is intended primarily for researchers and graduate students in mathematics, computer sciences, and electrical and other engineering departments. Readers with a background in advanced calculus and linear algebra, as well as prior knowledge in the fundamentals of optimization (some convex analysis, optimality conditions, and duality), will be best prepared for the material.