Abstract
A linear cone program in which the cone is the direct product of second-order cones (Lorentz cones) is considered. For its solution, we propose a primal affine-scaling type method generalizing the corresponding method used in linear programming. The method can be considered as a special way to solve a system of necessary and sufficient optimality conditions for a pair of mutually dual cone programs. These conditions are used to derive the dependence of the dual variables on the primal variables, and the dependence is substituted into the complementarity condition. The obtained system of equations is solved with respect to the primal variables by the fixed-point iteration method. The starting points in the method belong to the cone but do not necessarily satisfy the linear equality-type constraints. The local linear convergence of the method is proved under the assumption that the solutions of the primal and dual problems are nondegenerate and strictly complementary.
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 callMore From: Proceedings of the Steklov Institute of Mathematics
Disclaimer: 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.
