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Vector Lyapunov functions for nonconvex constrained optimization

  • Torbjørn Cunis
  • Ilya Kolmanovsky
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Abstract

Nonconvex constrained optimization problems are commonly solved by a Newton method for necessary conditions (sequential linear/quadratic programming) or a barrier reformulation (interior-point methods). We present a vector Lyapunov analysis for Newton-type algorithms based on constraint violation and optimality of the primal solutions to a sequence of approximate optimization problems. We thus prove local stability and convergence by constructing a strict Lyapunov function for the primal solution.

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Cite

BibTeXRIS
BibTeX
@misc{cunis2026vector,
  title = {{Vector Lyapunov functions for nonconvex constrained optimization}},
  author = {Torbjørn Cunis and Ilya Kolmanovsky},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.08729},
  eprint = {2611.08729},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.08729},
}
RIS
TY  - UNPB
TI  - Vector Lyapunov functions for nonconvex constrained optimization
AU  - Torbjørn Cunis
AU  - Ilya Kolmanovsky
PY  - 2026
DA  - 2026/11/05
PB  - arXiv
DO  - 10.48550/arxiv.2611.08729
UR  - https://arxiv.org/abs/2611.08729
AB  - Nonconvex constrained optimization problems are commonly solved by a Newton method for necessary conditions (sequential linear/quadratic programming) or a barrier reformulation (interior-point methods). We present a vector Lyapunov analysis for Newton-type algorithms based on constraint violation and optimality of the primal solutions to a sequence of approximate optimization problems. We thus prove local stability and convergence by constructing a strict Lyapunov function for the primal solution.
ER  -