Generalized Subdifferentials of Spectral Functions over Euclidean Jordan Algebras
نویسندگان
چکیده
منابع مشابه
Löwner's Operator and Spectral Functions in Euclidean Jordan Algebras
We study analyticity, differentiability, and semismoothness of Löwner’s operator and spectral functions under the framework of Euclidean Jordan algebras. In particular, we show that many optimization-related classical results in the symmetric matrix space can be generalized within this framework. For example, the metric projection operator over any symmetric cone defined in a Euclidean Jordan a...
متن کاملEuclidean Jordan Algebras and Generalized Aane-scaling Vector Elds
We describe the phase portrait of generalized aane-scaling vector elds for optimization problems involving symmetric cones. A Poisson structure on the complexiication of a real Jordan Euclidean algebra is introduced. Nonconstrained aane-scaling vector elds are proved to be Hamiltonian with respect to this Poisson structure. Constrained aane-scaling vector elds are obtained as a symplectic reduc...
متن کاملSpectral functions on Jordan algebras: differentiability and convexity properties
A spectral function on a formally real Jordan algebra is a real-valued function which depends only on the eigenvalues of its argument. One convenient way to create them is to start from a function f : R 7→ R which is symmetric in the components of its argument, and to define the function F (u) := f(λ(u)) where λ(u) is the vector of eigenvalues of u. In this paper, we show that this construction...
متن کاملSparse Recovery on Euclidean Jordan Algebras
We consider the sparse recovery problem on Euclidean Jordan algebra (SREJA), which includes sparse signal recovery and low-rank symmetric matrix recovery as special cases. We introduce the restricted isometry property, null space property (NSP), and s-goodness for linear transformations in s-sparse element recovery on Euclidean Jordan algebra (SREJA), all of which provide sufficient conditions ...
متن کاملNewton’s Algorithm in Euclidean Jordan Algebras, with Applications to Robotics∗
We consider a convex optimization problem on linearly constrained cones in Euclidean Jordan algebras. The problem is solved using a damped Newton algorithm. Quadratic convergence to the global minimum is shown using an explicit step-size selection. Moreover, we prove that the algorithm is a smooth discretization of a Newton flow with Lipschitz continuous derivative.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: SIAM Journal on Optimization
سال: 2020
ISSN: 1052-6234,1095-7189
DOI: 10.1137/19m1245001