Abstract
The notion of central path plays a fundamental role in the development of interior point methods which, in turn, have become important tools for solving various optimization problems. The central path equation is algebraic in nature and is derived from the KKT optimality conditions of a certain logarithmic barrier problem; meanwhile, the primal variable portion of the very same central path can also be cast precisely as the integral curve, known as the affine scaling trajectory, of a certain gradient-type dynamical system. The justification is easy to establish in the context of linear programming. Though expected, the generalization of such a concept to semidefinite programming is not quite as obvious due to the difficulty of addressing noncommutativity in matrix multiplication. This paper revisits the dynamical system characterization of these flows and addresses the needed details for extension to semidefinite programming by means of a simple notion of operators and a specially defined inner product. F...
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
