SOC functions and their applications
type: Item
instance of: scholarly article
title: SOC functions and their applications
zbMATH Open document ID: 1423.90002
DOI: 10.1007/978-981-13-4077-2
author: Jein-Shan Chen
published in: Springer Optimization and Its Applications
publication date: 2019-02-15T00:00:00Z
review text: Second-order cone optimization problems are one central topic in recent research. Chapter 1 and 2 are used to explain main properties of second-order cones (SOC) as spectral decomposition, analysis of SOC functions and trace functions, SOC convexity and monotonicity. For solving SOC problems, the author suggests in Chapter 3 a proximal-like, an interior proximal-like and an interior proximal method. Convergence of these methods is shown. The content of the monograph is completed by the investigation of SOC mean values, SOC inequalities, $r$-convex and $r$-quasiconvex functions in Chapters 4 and 5. The theory is presented, using a large number of carefully proven theorems and propositions. All of them are complemented and illustrated by examples showing the need for the used assumptions.
reviewed by: Stephan Dempe
Mathematics Subject Classification ID: 90-02
Mathematics Subject Classification ID: 90C25
Mathematics Subject Classification ID: 65K05
zbMATH DE Number: 7024139
zbMATH Keywords: second-order cones
zbMATH Keywords: second-order functions
zbMATH Keywords: second-order convexity
zbMATH Keywords: proximal-like algorithm
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1007/978-981-13-4077-2
OpenAlex ID: W2912906782
description: scientific article; zbMATH DE number 7024139