SOC Means and SOC Inequalities

Abstract

In this chapter, we present some other types of applications of the aforementioned SOC-functions, SOC-convexity, and SOC-monotonicity. These include so-called SOC means, SOC weighted means, and a few SOC trace versions of Young, Hölder, Minkowski inequalities, and Powers–Størmer’s inequality. We believe that these results will be helpful in convergence analysis of optimizations involved with SOC. Many materials of this chapter are extracted from [36, 77, 78], the readers can look into them for more details.