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The article introduces the adaptive versions of the Erroneous Conditional Gradient (ECG) algorithm with an Erroneous Oracle (EO) and a Linear Minimization Oracle (LMO) on a box-constrained feasible set. Two step-size strategies are studied: the first one displaying a dependency on the iteration, while the second one depends on the L-smoothness constant. This paper highlights the results of the implementation of these algorithms tested through computational experiments. PageRank is chosen for the algorithms to be applied to the optimization problem since the complexity of the former remains relevant even nowadays. The quality of the solution aligns with the theoretical expectations. Further research and practical implications of these algorithms are discussed in the conclusion.

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Adaptive Variants of Frank-Wolfe Method with Relative Inexact Gradient Information

  • 会议论文

  • 发表日期：

    2025年

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  • Gennady Denisov,
  • Fedor Stonyakin,
  • Mohammad Alkousa

摘要

The article introduces the adaptive versions of the Erroneous Conditional Gradient (ECG) algorithm with an Erroneous Oracle (EO) and a Linear Minimization Oracle (LMO) on a box-constrained feasible set. Two step-size strategies are studied: the first one displaying a dependency on the iteration, while the second one depends on the L-smoothness constant. This paper highlights the results of the implementation of these algorithms tested through computational experiments. PageRank is chosen for the algorithms to be applied to the optimization problem since the complexity of the former remains relevant even nowadays. The quality of the solution aligns with the theoretical expectations. Further research and practical implications of these algorithms are discussed in the conclusion.