Bregman Distance and Strong Convergence of Proximal-Type Algorithms
نویسندگان
چکیده
منابع مشابه
Strong Proximal Continuity and Convergence
and Applied Analysis 3 that the function f : (X, α) → (Y, β) is strongly proximally continuous on A if ∀E ⊂ A, ∀S ⊂ X, EαS ⇒ f (E) βf (S) . (5) Finally, one says that f is strongly proximally continuous on B if f is strongly proximally continuous on A, for every A ∈ B. We shall use the notation C B (X, Y) to denote the family of the functions from X to Y which are strongly proximally continuou...
متن کاملProximal-Like Incremental Aggregated Gradient Method with Linear Convergence under Bregman Distance Growth Conditions
We introduce a unified algorithmic framework, called proximal-like incremental aggregated gradient (PLIAG) method, for minimizing the sum of smooth convex component functions and a proper closed convex regularization function that is possibly non-smooth and extendedvalued, with an additional abstract feasible set whose geometry can be captured by using the domain of a Legendre function. The PLI...
متن کاملConvergence of Proximal-Like Algorithms
We analyze proximal methods based on entropy-like distances for the minimization of convex functions subject to nonnegativity constraints. We prove global convergence results for the methods with approximate minimization steps and an ergodic convergence result for the case of finding a zero of a maximal monotone operator. We also consider linearly constrained convex problems and establish a qua...
متن کاملApproximate iterations in Bregman-function-based proximal algorithms
This paper establishes convergence of generalized Bregman-function-based proximal point algorithms when the iterates are computed only approximately. The problem being solved is modeled as a general maximal monotone operator, and need not reduce to minimization of a function. The accuracy conditions on the iterates resemble those required for the classical "linear" proximal point algorithm, but...
متن کاملOn Uniform Convexity, Total Convexity and Convergence of the Proximal Point and Outer Bregman Projection Algorithms in Banach Spaces
In this paper we study and compare the notions of uniform convexity of functions at a point and on bounded sets with the notions of total convexity at a point and sequential consistency of functions, respectively. We establish connections between these concepts of strict convexity in infinite dimensional settings and use the connections in order to obtain improved convergence results concerning...
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: Abstract and Applied Analysis
سال: 2013
ISSN: 1085-3375,1687-0409
DOI: 10.1155/2013/590519