On the sensitivity of the optimal partition for parametric second-order conic optimization
Abstract
In this paper, using an optimal partition approach, we study the parametric analysis of a second-order conic optimization problem, where the objective function is perturbed along a fixed direction. We characterize the notions of so-called invariancy set and nonlinearity interval, which serve as stability regions of the optimal partition. We then propose, under the strict complementarity condition, an iterative procedure to compute a nonlinearity interval of the optimal partition. Furthermore, under primal and dual nondegeneracy conditions, we show that a boundary point of a nonlinearity interval can be numerically identified from a nonlinear reformulation of the parametric second-order conic optimization problem. Our theoretical results are supported by numerical experiments.
Cite
@article{arxiv.1910.03684,
title = {On the sensitivity of the optimal partition for parametric second-order conic optimization},
author = {Ali Mohammad-Nezhad and Tamas Terlaky},
journal= {arXiv preprint arXiv:1910.03684},
year = {2021}
}