Given a convex objective function on a Banach space, which is Lipschitz on bounded sets, we consider the class of regular vector fields introduced in our previous work on descent methods. We analyze the behaviour of the values of the objective function for two iterative processes generated by a regular vector field in the presence of computational errors and show that if the computational errors tend to zero, then the values of the objective function converge to its infimum.

中文翻译：

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Banach空间中正则向量场生成的两个迭代过程

给定 Banach 空间上的凸目标函数，即有界集上的 Lipschitz，我们考虑在我们之前关于下降方法的工作中引入的正则向量场类。我们分析了在存在计算误差的情况下由规则向量场生成的两个迭代过程的目标函数值的行为，并表明如果计算误差趋于零，则目标函数的值收敛到其下确界。