Proximal Minimization Methods with Generalized Bregman Functions
نویسندگان
چکیده
منابع مشابه
Proximal Point Methods with Bregman Function on Riemannian Manifolds
We study the proximal point algorithm with Bregman type distance to minimize the problem , , . ) ( min S x to s x f ∈ where S is an open convex subset of a complete simply connected Riemannian manifold M of non positive sectional curvature and f is a convex function in this manifold. Introducing a strong assumption on the geodesic triangle on this manifold we obtain the convergence of the seque...
متن کاملProximal Point Methods for Quasiconvex and Convex Functions With Bregman Distances on Hadamard Manifolds
This paper generalizes the proximal point method using Bregman distances to solve convex and quasiconvex optimization problems on noncompact Hadamard manifolds. We will proved that the sequence generated by our method is well defined and converges to an optimal solution of the problem. Also, we obtain the same convergence properties for the classical proximal method, applied to a class of quasi...
متن کاملGeneralized Kullback-Leibler Divergence Minimization within a Scaled Bregman Framework
The generalized Kullback-Leibler divergence (K-Ld) in Tsallis statistics subjected to the additive duality of generalized statistics (dual generalized K-Ld) is reconciled with the theory of Bregman divergences for expectations defined by normal averages, within a measure theoretic framework. Specifically, it is demonstrated that the dual generalized K-Ld is a scaled Bregman divergence. The Pyth...
متن کاملJoint minimization with alternating Bregman proximity operators
A systematic study of the proximity properties of Bregman distances is carried out. This investigation leads to the introduction of a new type of proximity operator which complements the usual Bregman proximity operator. We establish key properties of these operators and utilize them to devise a new alternating procedure for solving a broad class of joint minimization problems. We provide a com...
متن کاملProximal Minimization with Bregman Distances and the Goldstein-Osher Algorithm for Constrained Optimization
We consider here the problem of minimizing a convex function h : RK → R over x with T (x) = 0, where T : RK → RM is (possibly) nonlinear. We examine first the split-Bregman iterative algorithm proposed by Goldstein and Osher for L1 regularized image reconstruction, and then turn to proximal minimization algorithms (PMA) with Bregman distances, sometimes called Bregman iteration. The PMA form a ...
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 Control and Optimization
سال: 1997
ISSN: 0363-0129,1095-7138
DOI: 10.1137/s0363012995281742