On the Behavior of the Homogeneous Self-Dual Model for Conic Convex Optimization
Name
OR 372-04.pdf
Size
190.22 KB
Format
Adobe PDF
Checksum (MD5)
818af32f55988de82285b0c5e50cb720
Author(s)
Freund, Robert M.
Date Issued
October 2004
Publisher
Massachusetts Institute of Technology, Operations Research Center
Series/Report no.
Operations Research Center Working Paper Series;OR 372-04
Abstract
There is a natural norm associated with a starting point of the homogeneous self-dual (HSD) embedding model for conic convex optimization. In this norm
two measures of the HSD model’s behavior are precisely controlled independent of the problem instance: (i) the sizes of ε-optimal solutions, and (ii) the maximum distance of ε-optimal solutions to the boundary of the cone of the HSD variables. This norm is also useful in developing a stopping-rule theory for HSD-based interior-point methods such as SeDuMi. Under mild assumptions, we show that a standard stopping rule implicitly involves the sum of the sizes of the ε-optimal primal and dual solutions, as well as the size of the initial
primal and dual infeasibility residuals. This theory suggests possible criteria for developing starting points for the homogeneous self-dual model that might improve the resulting solution time in practice
MIT Department
Massachusetts Institute of Technology. Operations Research Center
Persistent DSpace Link
