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<p>In this work, we present and analyze a variant of the classical gradient method in Hilbert spaces for solving vector optimization problems where the objective function is Fréchet differentiable with <i>L</i>-Lipschitz continuous Jacobian map. The proposed algorithm utilizes a hybrid scheme involving a subproblem based on first-order information of the objective function and a projection step onto the intersection of two specific sets, which are constructed iteratively. This projection step ensures that the generated sequence exhibits strong convergence to a weakly efficient solution. Furthermore, a numerical experiment is provided to evaluate the practical performance of the Hybrid Vector Gradient Method (HVGM) based on the developed theory.</p>

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A hybrid gradient method for vector optimization problems

  • 期刊论文

  • 发表日期：

    2025年1月27日

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  • Ray Serra,
  • Sandoel Vieira

摘要

In this work, we present and analyze a variant of the classical gradient method in Hilbert spaces for solving vector optimization problems where the objective function is Fréchet differentiable with L-Lipschitz continuous Jacobian map. The proposed algorithm utilizes a hybrid scheme involving a subproblem based on first-order information of the objective function and a projection step onto the intersection of two specific sets, which are constructed iteratively. This projection step ensures that the generated sequence exhibits strong convergence to a weakly efficient solution. Furthermore, a numerical experiment is provided to evaluate the practical performance of the Hybrid Vector Gradient Method (HVGM) based on the developed theory.