Limiting behaviour and analyticity of weighted central paths in semidefinite programming

• Published in: Optimization methods & software Vol. 25; no. 2; pp. 247 - 262
• Main Authors: Halicka, Margareta, Trnovska, Maria
• Format: Journal Article
• Language: English
• Published: Abingdon Taylor & Francis 01.04.2010; Taylor & Francis Ltd
• Subjects: analyticity; interior-point methods; Semidefinite programming; Studies; weighted central path
• ISSN: 1055-6788; 1029-4937
• DOI: 10.1080/10556780903239493

This paper studies limiting behaviour of infeasible weighted central paths in semidefinite programming under strict complementarity assumption. It is known that weighted central paths associated with the 'Cholesky factor' symmetrization of the μ-parameterized centring condition are well defined for some classes of weight matrices, and they are analytic functions of μ for μ>0, sufficiently small. In this paper, we show that these paths, considered as functions of √μ, can be analytically extended to μ=0. Moreover, we show that the paths are analytic functions of μ at μ=0 if and only if the weight matrix is block diagonal in terms of the optimal block partition of variables.