Subgradient Method with Polyak’s Step in Transformed Space
We consider two subgradient methods (methods A and B) for finding the minimum point of a convex function for the known optimal value of the function. Method A is a subgradient method, which uses the Polyak’s step in the original space of variables. Method B is a subgradient method in the transformed space of variables, which uses Polyak’s step in the transformed space. For both methods a proof of the convergence of finding the minimum point with a given accuracy by the value of the function was performed. Examples of ravine convex (smooth and non-smooth) functions are given, for which convergence of method A is slow. It is shown that with a suitable choice of the space transformation matrix method B can be significantly accelerated in comparison with method A for ravine convex functions.
KeywordsSubgradient method Polyak’s step Space transformation
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