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.

在本文中，我们使用最优划分方法研究了目标函数沿固定方向扰动的二阶圆锥优化问题的参数分析。我们描述了所谓的不变集和非线性区间的概念，它们作为最优分区的稳定区域。然后，在严格互补条件下，我们提出了一个迭代程序来计算最优分区的非线性区间。此外，在原始和对偶非简并条件下，我们表明非线性区间的边界点可以从参数二阶圆锥优化问题的非线性重构中数值识别。我们的理论结果得到了数值实验的支持。