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A new simultaneous subgradient projection algorithm for solving a multiple-sets split feasibility problem. (English) Zbl 1313.90219

The paper presents a new algorithm for solving a multiple-sets split feasibility problem (MSSFP), a problem to find a point in the intersection of a family of closed convex sets in one space such that its image under a linear transformation lies in the intersection of another family of closed convex sets in the image space. Such a problem has broad application, e.g., in image reconstruction and signal processing.
The simultaneous subgradient projection algorithm for MSSFB by Y. Censor et al. [J. Math. Anal. Appl. 327, No. 2, 1244–1256 (2007; Zbl 1253.90211)] depends on the Lipschitz constant of the subgradient of the so-called proximity function. The authors propose an extrapolated subgradient projection algorithm where the step-size depends on an extrapolated parameter. The proposed algorithm does not depend on the estimate of the Lipschitz constant and possesses a variable step size at each iteration. The authors establish convergence results under mild assumptions and by means of numerical experiments illustrate convergence in fewer iterations compared to the algorithm by Censor et al. [loc. cit.].

MSC:

90C30 Nonlinear programming
90C33 Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming)
65K05 Numerical mathematical programming methods

Citations:

Zbl 1253.90211
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References:

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