عنوان

First-order methods in optimization /

1611974992

9781611974997

9781611974980

MO25

SIAM

First-order methods in optimization /

[Book]

Amir Beck, Technion-Israel Institute for Technology, Technion, Haifa, Israel.

Philadelphia, Pennsylvania :

Society for Industrial and Applied Mathematics (SIAM, 3600 Market Street, Floor 6, Philadelphia, PA 19104),

[2017]

1709

1 online resource (x, 484 pages).

MOS-SIAM series on optimization ;

25

Includes bibliographical references and index.

Vector spaces -- Extended real-value functions -- Subgradients -- Conjugate functions -- Smoothness and strong convexity -- The proximal operator -- Spectral functions -- Primal and dual projected subgradient methods -- Mirror descent -- The proximal gradient method -- The block proximal gradient method -- Dual-based proximal gradient methods -- The generalized Conditional gradient method -- Alternating minimization -- ADMM.

0

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 storage. The 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 books. First-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 methods.

First-order methods in optimization

9781611974980

Convergence.

Mathematical optimization.

Convergence.

Mathematical optimization.

Beck, Amir

Society for Industrial and Applied Mathematics,publisher.

20200823050106.0

rda

[Book]

Y