SOC functions and their applications
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.
scientific article; zbMATH DE number 7024139