基于非 Lipschitz 步长策略的临近分裂可行问题的强收敛性研究

Abstract

Abstract:

In this paper, An inertial viscosity-type algorithm is proposed to solve proximal split feasibility problems in Hilbert spaces. In this algorithm, a non-Lipschitz stepsize rule is given, which overcomes the drawback that the stepsize tends to zero. Further, a strong convergence theorem for our proposed algorithm is established without Lipschitz continuity of the gradient operators. As theoretical applications, the split equilibrium problem is investigated. Finally, numerical experiments are provided for demonstration and comparison.

Key words: Proximal split feasibility problem, Split equilibrium problem, Non-Lipschitz continuity, Viscosity-type algorithm, Strong convergence

CLC Number:

Ma Xiaojun, Chen Fu, Jia Zhifu. Research on a Strong Convergence Theorem for Proximal Split Feasibility Problems with Non-Lipschitz Stepsizes[J].Acta mathematica scientia,Series A, 2024, 44(4): 1052-1065.

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Research on a Strong Convergence Theorem for Proximal Split Feasibility Problems with Non-Lipschitz Stepsizes

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