An adaptive analog of Nesterov’s method for variational inequalities with a strongly monotone operator is proposed. The main idea of the method is an adaptive choice of constants in the maximized concave functionals at each iteration. In this case there is no need in specifying exact values of the constants, since this method makes it possible to find suitable constants at each iteration. Some estimates for the parameters determining the quality of the solution to the variational inequality are obtained as functions of the number of iterations.

中文翻译：

---

具有强单调算子的Nesterov方法的变分不等式的自适应模拟

提出了具有强烈单调算子的Nesterov变分不等式方法的自适应模拟。该方法的主要思想是在每次迭代时自适应选择最大化凹函数中的常数。在这种情况下，不需要指定常数的精确值，因为这种方法可以在每次迭代中找到合适的常数。获得一些参数估计，这些参数确定了变分不等式的解的质量，作为迭代次数的函数。