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<p>We focus on the optimization problem with smooth, possibly nonconvex objectives and a convex constraint set for which the Euclidean projection operation is practically available. Focusing on this setting, we carry out a general convergence and complexity analysis for algorithmic frameworks. Consequently, we discuss theoretically sound strategies to integrate momentum information within classical projected gradient-type algorithms. One of these approaches is then developed in detail, up to the definition of a tailored algorithm with both theoretical guarantees and reasonable per-iteration cost. The proposed method is finally shown to outperform the standard (spectral) projected gradient method in two different experimental benchmarks, indicating that the addition of momentum terms is as beneficial in the constrained setting as it is in the unconstrained scenario.</p>

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Projected Gradient Methods with Momentum

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年7月3日

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  • Matteo Lapucci,
  • Giampaolo Liuzzi,
  • Stefano Lucidi,
  • Marco Sciandrone,
  • Diego Scuppa

摘要

We focus on the optimization problem with smooth, possibly nonconvex objectives and a convex constraint set for which the Euclidean projection operation is practically available. Focusing on this setting, we carry out a general convergence and complexity analysis for algorithmic frameworks. Consequently, we discuss theoretically sound strategies to integrate momentum information within classical projected gradient-type algorithms. One of these approaches is then developed in detail, up to the definition of a tailored algorithm with both theoretical guarantees and reasonable per-iteration cost. The proposed method is finally shown to outperform the standard (spectral) projected gradient method in two different experimental benchmarks, indicating that the addition of momentum terms is as beneficial in the constrained setting as it is in the unconstrained scenario.