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Abstract <p> The paper considers the standard Levitin–Polyak conditional gradient algorithm for finding the minimum of a function with a Lipschitz continuous gradient on a convex compact set. It is shown that a sufficient condition for the linear convergence of the method is the support condition of strong convexity at the minimum point of the problem. The obtained result weakens the previously known conditions on the set that ensure the linear convergence, for example, the strong convexity of the constraint set. The convexity of the minimized function is not assumed. </p> <p> The work is theoretical in nature. </p>

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Support Condition of Strong Convexity and the Convergence of the Conditional Gradient Method

  • 期刊论文

  • 发表日期：

    2025年6月1日

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  • M. V. Balashov

摘要

Abstract

The paper considers the standard Levitin–Polyak conditional gradient algorithm for finding the minimum of a function with a Lipschitz continuous gradient on a convex compact set. It is shown that a sufficient condition for the linear convergence of the method is the support condition of strong convexity at the minimum point of the problem. The obtained result weakens the previously known conditions on the set that ensure the linear convergence, for example, the strong convexity of the constraint set. The convexity of the minimized function is not assumed.

The work is theoretical in nature.