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<p>In this paper, we investigate the second-order optimality conditions of sparsity-constrained optimization problems under the Fréchet second-order subdifferential of its Lagrangian function assumption instead of the twice continuous differentiability of the objective and the constraint functions. The second-order necessary optimality conditions of the sparse optimization problem are established under suitable Robinson constraint qualifications. Further, the second-order sufficient optimality conditions of the sparse optimization problem with equality constraints are also derived under mild conditions. The results presented in this paper extend the second-order optimality conditions [SIAM J. Optim. 2, 766-784 (2023)] to sparse optimization.</p>

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Second-Order Optimality Conditions for Sparse Optimization via Fréchet Second-Order Subdifferential

  • 期刊论文

  • 发表日期：

    2026年4月25日

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  • Jiawei Chen,
  • Yiran Wang,
  • Yibing Lv,
  • Jen-Chih Yao

摘要

In this paper, we investigate the second-order optimality conditions of sparsity-constrained optimization problems under the Fréchet second-order subdifferential of its Lagrangian function assumption instead of the twice continuous differentiability of the objective and the constraint functions. The second-order necessary optimality conditions of the sparse optimization problem are established under suitable Robinson constraint qualifications. Further, the second-order sufficient optimality conditions of the sparse optimization problem with equality constraints are also derived under mild conditions. The results presented in this paper extend the second-order optimality conditions [SIAM J. Optim. 2, 766-784 (2023)] to sparse optimization.