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 - <p style="text-align: justify;">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.</p>