A Unifying Optimal Partition Approach to Sensitivity Analysis in Conic Optimization∗

We study convex conic optimization problems in which the right-hand side and the cost vectors vary linearly as a function of a scalar parameter. We present a unifying geometric framework that subsumes the concept of the optimal partition in linear programming (LP) and semidefinite programming (SDP) and extends it to conic optimization. Similar to the optimal partition approach to sensitivity analysis in LP and SDP, the range of perturbations for which the optimal partition remains constant can be computed by solving two conic optimization problems. Under a weaker notion of ∗Revised version of the former technical report “On Sensitivity Analysis in Conic Programming” dated October 22, 2001. †Department of Applied Mathematics and Statistics, Stony Brook University, Stony Brook, NY 11794-3600, USA. The author is supported in part by NSF through CAREER grant DMI-0237415. ([email protected]) 1 nondegeneracy, this range is simply given by a minimum ratio test. We briefly discuss the properties of the optimal value function under such perturbations.