Parametric analysis of semidefinite optimization
Parametric analysis of semidefinite optimization
复制标题
半定优化的参数分析
作者：
Ali Mohammad;T. Terlaky
本文研究了目标函数摄动下半定优化问题的参数分析问题。研究了非线性区间上最优划分和最优集映射的性质。此外，我们还研究了Mohammad-Nezhad和Terlaky最近研究的非线性区间中最优划分近似的敏感性。通过在中心路径上或中心路径附近的有界内解序列，得到了最优划分的近似。我们导出了原问题和扰动问题的最优划分的逼近之间距离的上界。最后，我们用实验的方式检验了理论界限。
ABSTRACT In this paper, we study parametric analysis of semidefinite optimization problems w.r.t. the perturbation of the objective function. We study the behaviour of the optimal partition and optimal set mapping on a so-called nonlinearity interval. Furthermore, we investigate the sensitivity of the approximation of the optimal partition in a nonlinearity interval, which has been recently studied by Mohammad-Nezhad and Terlaky. The approximation of the optimal partition was obtained from a bounded sequence of interior solutions on, or in a neighbourhood of the central path. We derive an upper bound on the distance between the approximations of the optimal partitions of the original and perturbed problems. Finally, we examine the theoretical bounds by way of experimentation.