Two properties of condition numbers for convex programs via implicitly defined barrier functions

We study two issues on condition numbers for convex programs: one has to do with the growth of the condition numbers of the linear equations arising in interior-point algorithms; the other deals with solving conic systems and estimating their distance to infeasibility. These two issues share a common ground: the key tool for their development is a simple, novel perspective based on implicitly-defined barrier functions. This tool has potential use in optimization beyond the context of condition numbers.