Parametric analysis of semidefinite optimization. (2nd January 2020)

• Record Type: Journal Article
• Authors: Mohammad-Nezhad, Ali; Terlaky, Tamás
• Is Part Of: Optimization. Volume 69:Number 1(2020)
• Page Start: 187
• Page End: 216
• Publication Date: 2020-01-02
• Subjects: Parametric semidefinite optimization -- optimal partition -- nonlinearity interval -- maximally complementary solution; 90C51 -- 90C22 -- 90C25; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2019.1671382
• Languages: English
• ISSNs: 0233-1934

Abstract

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.