We use techniques originating from the subdiscipline of mathematical logic called ‘proof mining’ to provide rates of metastability and—under a metric regularity assumption—rates of convergence for a subgradient-type algorithm solving the equilibrium problem in convex optimization over fixed-point sets of firmly nonexpansive mappings. The algorithm is due to H. Iiduka and I. Yamada who in 2009 gave a noneffective proof of its convergence. This case study illustrates the applicability of the logic-based abstract quantitative analysis of general forms of Fejér monotonicity as given by the second author in previous papers.

中文翻译：

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平衡问题的一种次梯度方法的定量分析

我们使用源自称为“证明挖掘”的数学逻辑子学科的技术来提供亚稳态率和（在度量规则性假设下）次梯度型算法的收敛率，该算法解决定点集上的凸优化中的平衡问题牢固的非扩展映射。该算法归功于 H. Iiduka 和 I. Yamada，他们在 2009 年给出了其收敛性的无效证明。该案例研究说明了第二作者在以前的论文中给出的基于逻辑的抽象定量分析 Fejér 单调性的一般形式的适用性。