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New estimate for the curvature of an order-convex set and related questions

Ramazanov Ali B.

Control and Cybernetics

2020

Vol. 49, No. 2

233--240

It is well known that in discrete optimization problems, gradient (local) algorithms do not always guarantee an optimal solution. Therefore, the problem arises of finding the accuracy of the gradient algorithm. This is a fairly well-known problem and numerous publications have been devoted to it. In establishing accuracy, various approaches are used. One of these approaches is to obtain guaranteed estimates of the accuracy of the gradient algorithm in terms of the curvature of the admissible domain. With this approach, it is required to find the curvatures of the admissible region. Since finding the exact value of curvature is a difficult problem to solve, curvature estimates in terms of more or less simply calculated parameters of the problem are relevant. A new improved bound for the curvature of an order-convex set is found and is presented in this paper in terms of the steepness and parameters of strict convexity of the function.