We study the problem of finding a common element that solves the multiple-sets feasibility and equilibrium problems in real Hilbert spaces. We consider a general setting in which the involved sets are represented as level sets of given convex functions, and propose a constructible linear approximation scheme that involves the subgradient of the associated convex functions. Strong convergence of the proposed scheme is established under mild assumptions and several synthetic and practical numerical illustrations demonstrate the validity and advantages of our method compared with related schemes in the literature.

中文翻译：

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求解分裂逆问题的线性逼近方法及其应用

我们研究寻找一个共同元素来解决真实希尔伯特空间中的多集可行性和平衡问题的问题。我们考虑一个一般设置，其中所涉及的集合表示为给定凸函数的水平集，并提出了一种可构造的线性逼近方案，该方案涉及相关凸函数的次梯度。在温和的假设下建立了所提出方案的强收敛性，并且与文献中的相关方案相比，几个合成和实用的数值说明证明了我们的方法的有效性和优势。