[PDF] Top 20 A modified regularization method for finding zeros of monotone operators in Hilbert spaces

... algorithm [, ]. If A ≡ , then we obtain the proximal point algorithm [–] and if B ≡ , then we obtain the gradient method []. However, it is noted that the sequences generated by these schemes converge ... See full document

... maximal monotone operators is to find an efficient iterative algorithm to compute approximately zeroes of maximal monotone ...One method for finding zeros of maximal ... See full document

... of finding the fixed points of the nonlinear mappings, which is the subject of current interest in functional ...a method for finding a solution of the problem ...strongly monotone mapping and ... See full document

... of finding v ∈ E satisfying 0 ∈ Tv is connected with the convex minimization problems and variational ...maximal monotone, a well-known method for solving the equation 0 ∈ Tv in Hilbert space ... See full document

... maximal monotone operator and A is a continuous and monotone operator, we know that the operator A + B is a maximal monotone operator (see []), and hence one may try to find a solution of the ... See full document

... 18. Xu, HK: Averaged mappings and the gradient-projection algorithm. J. Optim. Theory Appl. 150, 360-378 (2011) 19. Hundal, H: An alternating projection that does not converge in norm. Nonlinear Anal. 57, 35-61 (2004) ... See full document

... Note that the inertial proximal algorithm was proposed by Alvarez 7 in the context of convex minimization. Afterwards, Alvarez and Attouch 8 considered its extension to maximal monotone operators. Recently, ... See full document

... In this paper, Kamimura and Takahashis convergence analysis [2] is extended to de- velop a generic convergence analysis which unifies a wide class of proximal-type methods applied to finding the zeroes of maximal ... See full document

... Many important problems have reformulations which require finding solutions of equi- libriums (.) and (.), for instance, image recovery, inverse problems, network alloca- tion, transportation problems and optimization ... See full document

... of monotone operators based on different regularization methods; see [–] and the references ...a regularization method for treating zero points of the sum of two monotone ... See full document

... for finding a common fixed point of a nonexpansive mapping and a strictly pseudocontractive ...of finding a common point of the set of fixed points of a nonexpansive mapping and the set of zeros of ... See full document

... its strong convergence. We also introduced an explicit iterative method as discretization of the implicit method. We proved that both the implicit and the explicit methods con- verge in norm to the same ... See full document

... We present the strong convergence theorem for the iterative scheme for finding a common element of the fixed-point set of a quasi-nonexpansive mapping and the zero set of the sums of maximal monotone ... See full document

... Huang, Strong convergence theorems for fixed point problems and generalized equilibrium problems of three relatively quasi-nonexpansive mappings in Banach spaces, J.. Zhou, Approximate p[r] ... See full document

... It follow from inequalities (9) and (10) above that in Hilbert spaces, nonextensive mappings are precisely the nonexpansive mapping and the strongly suppresive mappings are the strict contractions. For this ... See full document

... cover monotone inclusion problems, saddle point problems, variational inequality problems, minimization problems, Nash equilibria in noncooperative games, vector equilibrium problems, as well as certain fixed ... See full document

... cover monotone inclusion pro- blems, saddle point problems, variational inequality problems, minimization problems, optimization problems, variational inequality problems, vector equilibrium problems, Nash ... See full document

... the modified Helmholtz equation have been ...equation method has been proposed and a simplified Tikhonov regularization has been presented in ...Tikhonov regularization method to solve ... See full document

... continuous monotone mappings and a solution of the system of generalized equilibrium problems in a uniformly smooth and strictly convex real Banach space with the Kadec-Klee ... See full document

... Motivated by the above works, in this paper we introduce a general iterative scheme for approximating a point of F(T )∩ (A+B) –  ∩ G –  = ∅, where T is a λ-hybrid self-mapping on C, A : C → H is an α-inverse strongly ... See full document