SOC Functions and Their Applications

by Jein-Shan Chen

Overview

This book covers all of the concepts required to tackle second-order cone programs (SOCPs), in order to provide the reader a complete picture of SOC functions and their applications. SOCPs have attracted considerable attention, due to their wide range of applications in engineering, data science, and finance. To deal with this special group of optimization problems involving second-order cones (SOCs), we most often need to employ the following crucial concepts: (i) spectral decomposition associated with SOCs, (ii) analysis of SOC functions, and (iii) SOC-convexity and -monotonicity.

Moreover, we can roughly classify the related algorithms into two categories. One category includes traditional algorithms that do not use complementarity functions. Here, SOC-convexity and SOC-monotonicity play a key role. In contrast, complementarity functions are employed for the other category. In this context, complementarity functions are closely related to SOC functions; consequently, the analysis of SOC functions can help with these algorithms.

Product Details

ISBN-13:	9789811340765
Publisher:	Springer Nature Singapore
Publication date:	02/13/2019
Series:	Springer Optimization and Its Applications , #143
Edition description:	1st ed. 2019
Pages:	206
Product dimensions:	6.10(w) x 9.25(h) x (d)

Table of Contents

SOC Functions.- SOC-convexity and SOC-Monotonity.- Algorithmic Applications.- SOC Means and SOC Inequalities.- Possible Extensions.