Abstract
The paper proposes an inertial accelerated algorithm for solving split feasibility problem with multiple output sets. To improve the feasibility, the algorithm involves computing of projections onto relaxed sets (half spaces) instead of computing onto the closed convex sets, and it does not require calculating matrix inverse. To accelerate the convergence, the algorithm adopts self-adaptive rules and incorporates inertial technique. The strong convergence is shown under some suitable conditions. In addition, some newly derived results are presented for solving the split feasibility problem and split feasibility problem with multiple output sets. Finally, numerical experiments illustrate that the algorithm converges more quickly than some existing algorithms. Our results extend and improve some methods in the literature.
Highlights
Let H1 and H2 be two real Hilbert spaces and C and Q be nonempty, closed, and convex subsets of H1 and H2, respectively
We propose a new inertial self-adaptive relaxed CQ algorithm for solving the SFPwMOS (11) in general Hilbert spaces
Let C and Q be closed convex subsets of real Hilbert spaces H1 and H2, respectively, and f : H1 ⟶ R is given by f(x) (I − PQ)Ax2, where A : H1 ⟶ H2 be a bounded linear operator. en, for δ > 0 and x∗ ∈ H1, the following statements are equivalent
Summary
Let H1 and H2 be two real Hilbert spaces and C and Q be nonempty, closed, and convex subsets of H1 and H2, respectively. Many authors proposed algorithms that generate a sequence xk which converges strongly to a point in the solution set of the SFP (1), see, e.g., [9,10,11,12]. Where NC(x) is the normal cone of C at the point x We propose a new inertial self-adaptive relaxed CQ algorithm for solving the SFPwMOS (11) in general Hilbert spaces.
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