[PDF] Top 20 Convergence Analysis of General Version of Gauss Type Proximal Point Method for Metrically Regular Mappings

... the general version of Gauss-type proximal point al- gorithm (in short GG-PPA) for solving the inclusion 0 ∈ T x ( ) , where T is a set-valued mapping which is not necessarily ... See full document

... of mappings in variational analysis which goes deep in the roots of both theoretical and numerical ...is metrically regular (at any point in its graph) if and only if A maps X onto Y ... See full document

... this type of convergence result implies that d ( x k , j T − j 1 ( 0 )) → 0 almost surely ...local version of bounded linear regularity, a regularity condition which has been studied frequently in ... See full document

... Rochafellar’s proximal point algorithm ...modified proximal point algorithm by an additional projection at each step of ...the convergence of the sequence {x k } generated by the ... See full document

... a general algorithm for a countable family of nonexpansive mappings in Banach ...fixed point of a countable family of nonexpansive mappings which solves uniquely the corresponding variational ... See full document

... In this paper, we are interested in employing the iteration method (.) for a continuous mapping on an arbitrary interval. The iteration method was first introduced by Thianwan and Suantai [] as follows. ... See full document

... The concepts of weak commutativity, compatibility, noncompatibility and weak compatibility were frequently used to prove existence theorems in fixed and common fixed points for single and set-valued maps satisfying ... See full document

... Linear convergence of SGD for solving convex feasibility problems is proven recently in (Necoara, ...2017). Convergence analysis of SGD for minimizing an objective function subject to a finite number ... See full document

... Keywords -- Random Multivalued Operator, Asymptotically Regular, Random Fixed Point, Measurable Mapping.. INTRODUCTION.[r] ... See full document

... projection method and its variant forms, auxiliary problem prin- ciple, proximal-point algorithm and descent framework for solving variational inequal- ities and related optimization problems (see ... See full document

... Theorem 3.1 Let (Y, θ ) be a complete CAT(0) space and W be a nonempty closed con- vex subset. Let T : W → P (W ) be a multivalued mapping and P T be a nonexpansive mapping. Let h : Y → (– ∞ , ∞ ] be a proper convex and ... See full document

... After the paper of Branciari, a lot of a research works have been carried out on generalizing contractive conditions of integral type for different contractive mappings satisfying various known properties. ... See full document

... mixed type for two asymptotically nonexpansive self-mappings and two asymptotically nonexpansive nonself-mappings and prove strong and weak convergence theorems for the new two-step iterative ... See full document

... A complete CAT(0) space is often called an Hadamard space. We write (1 – t)x ⊕ ty for the unique point z in the geodesic segment joining from x to y such that d(x, z) = td(x, y) and d(y, z) = (1 – t)d(x, y). We ... See full document

... We introduce two modifications of the Mann iteration, by using the hybrid methods, for equilibrium and fixed point problems for an infinite family of asymptotically nonexpansive mappings in a Hilbert space. ... See full document

... One of the famous generalizations of the Banach contraction principle for the existence of fixed points for self mappings on metric spaces [5] is the theorem by Geraghty [8]. Consider A and B to be two nonempty ... See full document

... on Gauss-Newton numerical optimization method for fast ...descent method is used for the ...proposed method is observed during the training period as it converges quickly for the dataset used ... See full document

... Remark 1.1. It is clear that every nonexpansive mapping is asymptotically non- expansive and every asymptotically nonexpansive is uniformly Lipschitzian. Also, if F(T ) 6= ∅, then a nonexpansive mapping is a ... See full document

... fixed point theorem for l -hybrid mappings in Hilbert spaces in 2010 to this much wider class of nonlinear mappings in Banach ...weak convergence theorem for this new class of nonlinear ... See full document

... of convergence in a general metric space set- ting which he called ...fixed point for nonexpansive mapping, asymptotically nonexpansive mapping, nearly asymptotically nonexpansive, asymptoti- cally ... See full document