Parametric Semidefinite Programming: Geometry of the Trajectory of Solutions
成果类型：
Article
署名作者：
Bellon, Antonio; Henrion, Didier; Kungurtsev, Vyacheslav; Marec, Jakub
署名单位：
Czech Technical University Prague; Universite de Toulouse; Centre National de la Recherche Scientifique (CNRS)
刊物名称：
MATHEMATICS OF OPERATIONS RESEARCH
ISSN/ISSBN：
0364-765X
DOI：
10.1287/moor.2021.0097
发表日期：
2025
关键词：
摘要：
In many applications, solutions of convex optimization problems are updated on-line, as functions of time. In this paper, we consider parametric semidefinite programs, which are linear optimization problems in the semidefinite cone whose coefficients (input data) depend on a time parameter. We are interested in the geometry of the solution (output data) trajectory, defined as the set of solutions depending on the parameter. We propose an exhaustive description of the geometry of the solution trajectory. As our main result, we show that only six distinct behaviors can be observed at a neighborhood of a given point along the solution trajectory. Each possible behavior is then illustrated by an example.