2020/09/10 by M. Seetharama Gowda, Gowda, Muddappa
Computer Science · Mathematics · Medicine · #17C20 #17C30 #52A41 #90C26 #Advanced Topics in Algebra #Chronic Myeloid Leukemia Treatments #FOS: Mathematics #Functional Analysis (math.FA) #Matrix Theory and Algorithms #Optimization and Control (math.OC)
paper · pdf · doi:10.48550/arxiv.2009.04874
openalex publication_date 2020/09/10 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28
The commutation principle of Ramirez, Seeger, and Sossa proved in the setting\nof Euclidean Jordan algebras says that when the sum of a real valued function\nh and a spectral function \Φ is minimized/maximized over a spectral set\nE, any local optimizer a at which h is Fr 'echet differentiable\noperator commutes with the derivative h\′(a). In this paper, assuming\nthe existence of a subgradient in place the derivative (of h), we establish\n`strong operator commutativity' relations: If a solves the problem\n undersetE\max ,(h+\Φ), then a strongly operator commutes with every\nelement in the subdifferential of h at a; If E and h are convex and a\nsolves the problem undersetE\min ,h, then a strongly operator commutes\nwith the negative of some element in the subdifferential of h at a. These\nresults improve known (operator) commutativity relations for linear h and for\nsolutions of variational inequality problems. We establish these results via a\ngeometric commutation principle that is valid not only in Euclidean Jordan\nalgebras, but also in the broader setting of FTvN-systems.\n