Metastability of the proximal point algorithm with multi-parameters
نویسندگان
چکیده
منابع مشابه
On the contraction-proximal point algorithms with multi-parameters
In this paper we consider the contraction-proximal point algorithm: xn+1 = αnu+λnxn+γnJβnxn, where Jβn denotes the resolvent of a monotone operator A. Under the assumption that limn αn = 0, ∑ n αn = ∞, lim infn βn > 0, and lim infn γn > 0, we prove the strong convergence of the iterates as well as its inexact version. As a result we improve and recover some recent results by Boikanyo and Morosa...
متن کاملW-convergence of the proximal point algorithm in complete CAT(0) metric spaces
In this paper, we generalize the proximal point algorithm to complete CAT(0) spaces and show that the sequence generated by the proximal point algorithm $w$-converges to a zero of the maximal monotone operator. Also, we prove that if $f: Xrightarrow ]-infty, +infty]$ is a proper, convex and lower semicontinuous function on the complete CAT(0) space $X$, then the proximal...
متن کاملFinite termination of the proximal point algorithm
where q~ is a c losed, convex func t ion def ined on R n, having values in ~ and S is a c losed, convex set in ~n. We write S for the op t ima l so lu t ion set o f (1), S : = arg minxes cb(x) and assume this set to be non-empty , in o rde r tha t a p ro jec t ion o p e r a t i o n on to this set is well def ined. In o rde r to s impl i fy our analysis , let us define , b ~ ( x ) := ¢~(x )+~, (...
متن کاملA Hybrid Projection – Proximal Point Algorithm ∗
We propose a modification of the classical proximal point algorithm for finding zeroes of a maximal monotone operator in a Hilbert space. In particular, an approximate proximal point iteration is used to construct a hyperplane which strictly separates the current iterate from the solution set of the problem. This step is then followed by a projection of the current iterate onto the separating h...
متن کاملInexact Halpern-type proximal point algorithm
We present several strong convergence results for the modified, Halpern-type, proximal point algorithm xn+1 = αnu + (1 − αn)Jβn xn + en (n = 0, 1, . . .; u, x0 ∈ H given, and Jβn = (I + βn A)−1, for a maximal monotone operator A) in a real Hilbert space, under new sets of conditions on αn ∈ (0, 1) and βn ∈ (0,∞). These conditions are weaker than those known to us and our results extend and impr...
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: Portugaliae Mathematica
سال: 2020
ISSN: 0032-5155
DOI: 10.4171/pm/2054