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A Tight Surrogate-Based Adaptive Step Size for the Multiobjective Conditional Gradient Method — arXiv:2609.21831

Source: arXiv (en)
Original: https://arxiv.org/abs/2609.21831
License (as archived): CC0-1.0
Archived: 2026-10-10T02:04:47.475Z
SHA-256 of the archived text: c944fcd0e6f8d2015db870286d135d3d32395953bf03a9237f5a41aa2966f772
Stable URL of this page: https://metraipolis.com/documento/dc_ee451c3668bc

How to cite

A Tight Surrogate-Based Adaptive Step Size for the Multiobjective Conditional Gradient Method — arXiv:2609.21831 — arXiv (en), https://arxiv.org/abs/2609.21831 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_ee451c3668bc (Metraipolis archive dc_ee451c3668bc, sha256 c944fcd0e6f8d2015db870286d135d3d32395953bf03a9237f5a41aa2966f772)

BibTeX

@misc{dcee451c3668bc,
  title = {A Tight Surrogate-Based Adaptive Step Size for the Multiobjective Conditional Gradient Method — arXiv:2609.21831},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2609.21831},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_ee451c3668bc; sha256 c944fcd0e6f8d2015db870286d135d3d32395953bf03a9237f5a41aa2966f772},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2609.21831. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

The multiobjective conditional gradient (MCondG) method is an effective descent-type algorithm for solving constrained multiobjective optimization problems. In this algorithm, the adaptive step size is derived by minimizing a one-dimensional convex quadratic surrogate function, which guarantees a sufficient decrease in all objective functions at each iteration. However, we observe that this surrogate function is relatively conservative, producing overly small step sizes and consequently slowing the convergence of the algorithm. This conservativeness stems from the fact that the surrogate function is dominated by the largest Lipschitz constant among the gradients of all objective functions. Motivated by this observation, we develop a tighter quadratic surrogate function that exploits the individual gradient Lipschitz constants. Based on this surrogate, we propose a new adaptive step size strategy obtained by evaluating this surrogate over a finite candidate set. We prove that the proposed step size preserves the descent property of the MCondG method, and has an improved worst-case complexity bound compared with the original adaptive step size strategy. Numerical experiments on benchmark and real-world problems demonstrate the effectiveness of the proposed strategy in terms of computational efficiency and solution quality.

Tema degli esploratori: matematica e informatica teorica (retro-catalogo arXiv: annunci del 2026-09-21 in math.OC).
Categorie arXiv: Optimization and Control (math.OC).
Pagina del lavoro: https://arxiv.org/abs/2609.21831 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-10T01:45:31.244Z dalla pagina https://arxiv.org/catchup/math.OC/2026-09-21?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).