This paper develops an approach for solving convex feasibility problems where the constraints are given by the intersection of two convex cones in a Hilbert space. An extension to the feasibility problem for the intersection of two convex sets is presented as well. It is shown that one can solve such problems in a finite number of steps and an explicit upper bound for the required number of ste...

<p style='text-indent:20px;'>In this paper a dynamical system model is proposed for solving the split convex feasibility problem. Under mild conditions, it shown that globally converges to solution of An exponential convergence obtained provided bounded linear regularity property satisfied. The validity and transient behavior demonstrated by several numerical examples. method in can be re...

The convex feasibility problem CFP of finding a point in the nonempty intersection ⋂N i 1Ci is considered, where N 1 is an integer and the Ci’s are assumed to be convex closed subsets of a Banach space E. By using hybrid iterative methods, we prove theorems on the strong convergence to a common fixed point for a finite family of relatively nonexpansive mappings. Then, we apply our results for s...

In this paper we introduce a sequential block iterative method and its simultaneous version with op-timal combination of weights (instead of convex combination) for solving convex feasibility problems.When the intersection of the given family of convex sets is nonempty, it is shown that any sequencegenerated by the given algorithms converges to a feasible point. Additionally for linear feasibil...

The implicit convex feasibility problem attempts to find a point in the intersection of a finite family of convex sets, some of which are not explicitly determined but may vary. We develop simultaneous and sequential projection methods capable of handling such problems and demonstrate their applicability to image denoising in a specific medical imaging situation. By allowing the variable sets t...

We introduce a hybrid projection-localization method for solving large convex cone programs. The method interleaves a series of projections onto localization sets with the classical alternating projections method for convex feasibility problems; the problem is made amenable to the method by reducing it to a convex feasibility problem composed of a subspace and a cone via its homogeneous self-du...

We study the multiple-sets split feasibility problem that requires to find a point closest to a family of closed convex sets in one space such that its image under a linear transformation will be closest to another family of closed convex sets in the image space. By casting the problem into an equivalent problem in a suitable product space we are able to present a simultaneous subgradients proj...

The convex feasibility problem (CFP) is at the core of the modeling of many problems in various areas of science. Subgradient projection methods are important tools for solving the CFP because they enable the use of subgradient calculations instead of orthogonal projections onto the individual sets of the problem. Working in a real Hilbert space, we show that the sequential subgradient projecti...