In this article we use techniques of proof mining to analyse a result, due to Yonghong Yao and Muhammad Aslam Noor, concerning the strong convergence of a generalized proximal point algorithm which involves multiple parameters. Yao and Noor's result ensures the strong convergence of the algorithm to the nearest projection point onto the set of zeros of the operator. Our quantitative analysis, guided by Fernando Ferreira and Paulo Oliva's bounded functional interpretation, provides a primitive recursive bound on the metastability for the convergence of the algorithm, in the sense of Terence Tao. Furthermore, we obtain quantitative information on the asymptotic regularity of the iteration. The results of this paper are made possible by an arithmetization of the $\limsup$.

中文翻译：

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多参数近端点算法的亚稳定性

在本文中，我们使用证明挖掘技术来分析Yonghong Yao 和Muhammad Aslam Noor 提出的关于涉及多个参数的广义近点算法的强收敛性的结果。Yao 和 Noor 的结果确保了算法的强收敛性到最近的投影点到算子的零集上。我们的定量分析在 Fernando Ferreira 和 Paulo Oliva 的有界函数解释的指导下，在 Terence Tao 的意义上为算法的收敛性提供了一个关于亚稳态的原始递归边界。此外，我们获得了迭代渐近规律的定量信息。本文的结果是通过 $\limsup$ 的算术化实现的。