On the sensitivity of the optimal partition for parametric second-order conic optimization
成果类型：
Article
署名作者：
Mohammad-Nezhad, Ali; Terlaky, Tamas
署名单位：
Purdue University System; Purdue University; Lehigh University
刊物名称：
MATHEMATICAL PROGRAMMING
ISSN/ISSBN：
0025-5610
DOI：
10.1007/s10107-021-01690-7
发表日期：
2021
页码：
491-525
关键词：
摘要：
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.