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Some commutation principles for optimization problems over transformation groups and semi-FTvN systems

2025/03/11 by M. Seetharama Gowda, David Sossa, Gowda, M. Seetharama +1
Engineering · #15A27 #17C20 #46N10 #90C33 #FOS: Mathematics #Optimization and Control (math.OC) #Optimization and Packing Problems

paper · pdf · doi:10.48550/arxiv.2503.08654

openalex publication_date 2025/03/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We introduce the concepts of commutativity relative to a transformation group and strong commutativity in the setting of a semi-FTvN system and show their appearance as optimality conditions in certain optimization problems. In the setting of a semi-FTvN system (in particular, in an FTvN system), we show that strong commutativity implies commutativity and observe that in the special case of Euclidean Jordan algebra, commutativity and strong commutativity concepts reduce, respectively, to those of operator and strong operator commutativity. We demonstrate that every complete hyperbolic polynomial induces a semi-FTvN system. By way of an application, we describe several commutation principles.

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