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arXiv · 2611.08729

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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Torbjørn Cunis, Ilya Kolmanovsky. 2026-11-05. Vector Lyapunov functions for nonconvex constrained optimization. https://arxiv.org/abs/2611.08729

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