SOC Functions and Their Applications

Description

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. Front Matter ....Pages i-x SOC Functions (Jein-Shan Chen)....Pages 1-37 SOC-Convexity and SOC-Monotonity (Jein-Shan Chen)....Pages 39-99 Algorithmic Applications (Jein-Shan Chen)....Pages 101-158 SOC Means and SOC Inequalities (Jein-Shan Chen)....Pages 159-188 Possible Extensions (Jein-Shan Chen)....Pages 189-200 Back Matter ....Pages 201-206