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Volume 43, Issue 4
An SQP-Type Proximal Gradient Method for Composite Optimization Problems with Equality Constraints

Pinzheng Wei & Weihong Yang

DOI: 10.4208/jcm.2404-m2023-0128

J. Comp. Math., 43 (2025), pp. 1016-1044.

Published online: 2025-07

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  • Abstract

In this paper, we present an SQP-type proximal gradient method (SQP-PG) for composite optimization problems with equality constraints. At each iteration, SQP-PG solves a subproblem to get the search direction, and takes an exact penalty function as the merit function to determine if the trial step is accepted. The global convergence of the SQP-PG method is proved and the iteration complexity for obtaining an $\epsilon$-stationary point is analyzed. We also establish the local linear convergence result of the SQP-PG method under the second-order sufficient condition. Numerical results demonstrate that, compared to the state-of-the-art algorithms, SQP-PG is an effective method for equality constrained composite optimization problems.

  • Keywords

Composite optimization, Proximal gradient method, SQP method, Semi-smooth Newton method.

  • AMS Subject Headings

90C30, 65K05

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JCM-43-1016, author = {Wei , Pinzheng and Yang , Weihong}, title = {An SQP-Type Proximal Gradient Method for Composite Optimization Problems with Equality Constraints}, journal = {Journal of Computational Mathematics}, year = {2025}, volume = {43}, number = {4}, pages = {1016--1044}, abstract = {

In this paper, we present an SQP-type proximal gradient method (SQP-PG) for composite optimization problems with equality constraints. At each iteration, SQP-PG solves a subproblem to get the search direction, and takes an exact penalty function as the merit function to determine if the trial step is accepted. The global convergence of the SQP-PG method is proved and the iteration complexity for obtaining an $\epsilon$-stationary point is analyzed. We also establish the local linear convergence result of the SQP-PG method under the second-order sufficient condition. Numerical results demonstrate that, compared to the state-of-the-art algorithms, SQP-PG is an effective method for equality constrained composite optimization problems.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.2404-m2023-0128}, url = {http://global-sci.org/intro/article_detail/jcm/24269.html} }
TY - JOUR T1 - An SQP-Type Proximal Gradient Method for Composite Optimization Problems with Equality Constraints AU - Wei , Pinzheng AU - Yang , Weihong JO - Journal of Computational Mathematics VL - 4 SP - 1016 EP - 1044 PY - 2025 DA - 2025/07 SN - 43 DO - http://doi.org/10.4208/jcm.2404-m2023-0128 UR - https://global-sci.org/intro/article_detail/jcm/24269.html KW - Composite optimization, Proximal gradient method, SQP method, Semi-smooth Newton method. AB -

In this paper, we present an SQP-type proximal gradient method (SQP-PG) for composite optimization problems with equality constraints. At each iteration, SQP-PG solves a subproblem to get the search direction, and takes an exact penalty function as the merit function to determine if the trial step is accepted. The global convergence of the SQP-PG method is proved and the iteration complexity for obtaining an $\epsilon$-stationary point is analyzed. We also establish the local linear convergence result of the SQP-PG method under the second-order sufficient condition. Numerical results demonstrate that, compared to the state-of-the-art algorithms, SQP-PG is an effective method for equality constrained composite optimization problems.

Wei , Pinzheng and Yang , Weihong. (2025). An SQP-Type Proximal Gradient Method for Composite Optimization Problems with Equality Constraints. Journal of Computational Mathematics. 43 (4). 1016-1044. doi:10.4208/jcm.2404-m2023-0128
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