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Alternating Gradient-Type Algorithm for Bilevel Optimization with Inexact Lower-Level Solutions via Moreau Envelope–Based Reformulation

Xiaoning Bai et al.

SIAM Journal on Optimization2026https://doi.org/10.1137/24m1721049preprint
AJG 3
Weight
0.50

What the paper says

In this paper, we study a class of bilevel optimization problems where the lower-level problem is a convex composite optimization model, which arises in various applications, including bilevel hyperparameter selection for regularized regression models. To solve these problems, we propose an Alternating Gradient-type algorithm with Inexact Lower-level Solutions (AGILS) based on a Moreau envelope-based reformulation of the bilevel optimization problem. The proposed algorithm does not require exact solutions of the lower-level problem at each iteration, improving computational efficiency. We prove the convergence of AGILS to stationary points and, under the Kurdyka-Łojasiewicz (KL) property, establish its sequential convergence. Numerical experiments, including a toy example and a bilevel hyperparameter selection problem for the sparse group Lasso model, demonstrate the effectiveness of the proposed AGILS.

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https://doi.org/https://doi.org/10.1137/24m1721049

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@article{xiaoning2026,
  title        = {{Alternating Gradient-Type Algorithm for Bilevel Optimization with Inexact Lower-Level Solutions via Moreau Envelope–Based Reformulation}},
  author       = {Xiaoning Bai et al.},
  journal      = {SIAM Journal on Optimization},
  year         = {2026},
  doi          = {https://doi.org/https://doi.org/10.1137/24m1721049},
}

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Alternating Gradient-Type Algorithm for Bilevel Optimization with Inexact Lower-Level Solutions via Moreau Envelope–Based Reformulation

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Evidence weight

0.50

Balanced mode · F 0.40 / M 0.15 / V 0.05 / R 0.40

F · citation impact0.50 × 0.4 = 0.20
M · momentum0.50 × 0.15 = 0.07
V · venue signal0.50 × 0.05 = 0.03
R · text relevance †0.50 × 0.4 = 0.20

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