A modified dynamical system with time-varying coefficients for split feasibility problem

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Abstract
In this paper, a modified dynamical system is proposed to address the split feasibility problem. For any initial point, it is proved that the proposed approach converges in a fixed time. Furthermore, by introducing time-varying coefficients, the proposed method can be accelerated. It is shown that the settling time for the proposed fixed-time converging approach has a uniform upper bound for all initial conditions. The proposed approach has the advantage that it is robust against bounded vanishing perturbation. Numerical experiments on signal processing and image restoration tasks validate its effectiveness and demonstrate superior performance. These properties make the method particularly suitable for real-time applications—such as signal recovery and image enhancement—where both computational efficiency and predictable convergence are critical.

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