Lyapunov-type least-squares problems over symmetric cones
An exploration of the linear image of a symmetric cone under the Lyapunov operator as well as a characterization of necessary and\(\backslash\)or sufficient conditions for the solution existence and uniqueness of the Lyapunov-type least-squares problem over a symmetric cone are done. The paper is organized as follows: The first section is an introduction. Some basic concepts and properties on a Euclidean Jordan algebra and a symmetric cone are collected and developed, and several preliminaries on convex analysis are reviewed in Section 2. Some intrinsic features and properties of the cone \(L_a(K)\) are explored for some given \(a \in \mathcal{J}\) in the next section. Section 4 is devoted to the solvability and uniqueness of the Lyapunov-type least-squares problem over the symmetric cone. Some concluding remarks are drawn in Section 5.
scientific article; zbMATH DE number 6104553
scientific article