Resolvent average on second-order cone

Abstract

Recently Bauschke et al. introduced a very interesting and new notion of proximal average in the context of convex analysis, and studied this subject systemically in [3-7] from various viewpoints. In addition, this new concept was applied to positive semidefinite matrices under the name of resolvent average, and basic properties of the resolvent average are successfully established by themselves from a totally different view and techniques of convex analysis rather than the classical matrix diagonalization [8]. Inspired by their works and the well-known fact that the second-order cone is the other typical example of symmetric cone, we study the resolvent average on second-order cone, and derive corresponding results in a different manner from Bauschke et al. [8].