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PreprintCC BY 4.0arXiv

Stabilized SQP Method for Convex Piecewise Linear-Quadratic Composite Optimization Problems

  • Nguyen T. V. Hang
  • Ebrahim Sarabi
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Abstract

This paper addresses the local convergence analysis of the stabilized sequential quadratic programming method for a class of composite optimization problems with convex piecewise linear- quadratic (CPLQ) modeling functions. We demonstrate that an appropriate second-order sufficient condition (SOSC) -formulated for composite problems- alone is sufficient to guarantee local superlin- ear convergence of the primal-dual sequence generated by this method. Furthermore, we examine the relaxation of the SOSC and show that it can be replaced with a weaker noncriticality of the associated Lagrange multiplier, provided, the modeling function is polyhedral and a relative interior condition is satisfied. We also present counterexamples showing that the relative interior condition is indispensable and that this relaxation fails for general CPLQ modeling functions.

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Cite

BibTeXRIS
BibTeX
@misc{hang2026stabilized,
  title = {{Stabilized SQP Method for Convex Piecewise Linear-Quadratic Composite Optimization Problems}},
  author = {Nguyen T. V. Hang and Ebrahim Sarabi},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.13741},
  eprint = {2610.13741},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.13741},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Stabilized SQP Method for Convex Piecewise Linear-Quadratic Composite Optimization Problems
AU  - Nguyen T. V. Hang
AU  - Ebrahim Sarabi
PY  - 2026
DA  - 2026/10/09
PB  - arXiv
DO  - 10.48550/arxiv.2610.13741
UR  - https://arxiv.org/abs/2610.13741
AB  - This paper addresses the local convergence analysis of the stabilized sequential quadratic programming method for a class of composite optimization problems with convex piecewise linear- quadratic (CPLQ) modeling functions. We demonstrate that an appropriate second-order sufficient condition (SOSC) -formulated for composite problems- alone is sufficient to guarantee local superlin- ear convergence of the primal-dual sequence generated by this method. Furthermore, we examine the relaxation of the SOSC and show that it can be replaced with a weaker noncriticality of the associated Lagrange multiplier, provided, the modeling function is polyhedral and a relative interior condition is satisfied. We also present counterexamples showing that the relative interior condition is indispensable and that this relaxation fails for general CPLQ modeling functions.
ER  -