Extended commutation principles for normal decomposition systems

In this paper we study some optimization problems on Lewis' normal decomposition systems (1996, 2000). We extend Gowda and Jeong's commutation principle (2017) in two directions. Firstly, we replace the sum operation by an arbitrary binary operation monotone in each variable. Secondly, we employ G-increasing functions in place of G-invariant convex functions. We give applications to some classes of matrices. We also interpret the obtained results for simple Euclidean Jordan algebras.