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＜電子ブック＞
SOC Functions and Their Applications / by Jein-Shan Chen
(Springer Optimization and Its Applications. ISSN:19316836 ; 143)

版	1st ed. 2019.
出版者	(Singapore : Springer Nature Singapore : Imprint: Springer)
出版年	2019
本文言語	英語
大きさ	X, 206 p. 8 illus., 6 illus. in color : online resource
著者標目	*Chen, Jein-Shan author SpringerLink (Online service)
件　名	LCSH:Operations research LCSH:Management science FREE:Operations Research, Management Science
一般注記	SOC Functions -- SOC-convexity and SOC-Monotonity -- Algorithmic Applications -- SOC Means and SOC Inequalities -- Possible Extensions 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 HTTP:URL=https://doi.org/10.1007/978-981-13-4077-2

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