[PDF] Top 20 An iterative algorithm for fixed point problem and convex minimization problem with applications

... Remark . The convergence rate of the projection gradient method is at best linear. The linear convergence is attained with Polyak’s stepsize and for an objective function with a sharp set of minima. The linear ... See full document

... Theorem . Let C be a nonempty closed convex subset of a real Hilbert space H . For the minimization problem (.), assume that f is (Frechet) differentiable and the gradient ∇ f is a ... See full document

... new iterative algorithm for solving the split equality generalized mixed equilibrium ...As applications, we employ our results to get the convergence results for the split equality convex ... See full document

... an iterative algorithm to approximate a common solution of a generalized equilibrium problem and a fixed point problem for an asymptotically nonexpansive mapping in a real ... See full document

... Picard algorithm to the smooth convex minimization problem and point out that the Picard algorithm is the steepest descent method for solving the minimization ...Picard ... See full document

... and convex programming prob- lems; see ...explicit iterative schemes for computing a common element of the set of fixed points of a nonexpansive mapping and the set of solutions of the variational inequality ... See full document

... constrained convex minimization ...explicit iterative schemes based on the regularization for solving a constrained convex minimization ...the minimization problem. Such a ... See full document

... fixed point problem ...and convex programming problems; see ...fixed point problem; see ...convergence iterative algorithm to solve prob- lem ... See full document

... PDFP algorithm is built upon fixed point theory on the primal and dual ...Condat’s algorithm []. In addition, we point out that the ranges of the parameters in PDFP are larger than those of ... See full document

... converges strongly to a fixed point x ∗ of T, also the solution of a variational inequality. As a special case, this projection method solves some quadratic minimization problem. The results here ... See full document

... CQ algorithm is efficient to solve the prob- ...fixed point sets, the efficiency of the CQ algorithm will be affected because the projections onto such convex sets are generally hard to be ... See full document

... equilibrium problem with a relaxed monotone mapping and a countable family of nonexpansive mappings in a Hilbert space,” Fixed Point Theory and Applications, ... See full document

... an algorithm to accelerate the Halpern fixed point algorithm in a real Hilbert ...Halpern algorithm to the smooth convex minimization problem, which is an example of a fixed ... See full document

... solve convex minimization problems; see, for example, 1, 2 and the references ...typical problem is to minimize a quadratic function over the set of fixed points of a nonexpansive mapping on a ... See full document

... constrained convex minimization problem has been studied by several authors; see, for example [9] and the references ...to algorithm (6); namely an average mapping approach; see, for example ... See full document

... We assumed that θ ( ) t is a convex and differentiable function, which indicate one can apply the classical Newton-type algorithm directly. And the assumption θ ′ ( ) 0 > 0 means that 0 is not a ... See full document

... block iterative algorithm is a method which often used by many authors to solve the convex feasibility problem see, ...block iterative scheme to establish strong convergence theorems ... See full document

... an iterative method to approximate solutions of a hierarchical fixed point problem and a variational inequality problem involving a finite family of nonexpansive mappings on a real Hilbert ... See full document

... erative algorithm which has strong ...the convex minimization problem of finding a minimizer of a proper lower-semicontinuous convex function and the variational problem of ... See full document

... Corollary 4.1. Let H 1 , H 2 and H 3 be real Hilbert spaces and C ⊂ H 1 , Q ⊂ H 2 be nonempty, closed and convex sets. Let A : H 1 → H 3 , B : H 2 → H 3 be bounded linear operators with their adjoint operators A ∗ ... See full document