Abstract
In this survey, the problem of finding the minimal root to an equation is discussed. It is supposed that the equation under consideration can have many roots. In the case when the Lipschitz constant for the objective function or its first derivative is known a priori, two methods based on global optimization ideas are presented. The algorithms either find the minimal root or determine the global minimizers (in the case when the objective function has no roots). If the Lipschitz constants are unknown, there are introduced two methods adaptively estimating local Lipschitz constants during the search. This approach allows us to accelerate the search in comparison with the case with known a priori Lipschitz constants. Sufficient conditions for convergence of the new methods to the desired solution are established.
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