The purpose of this paper is to extend, as much as possible, the modern theory of condition numbers for conic convex optimization: z* :=minx ctx, s.t. Ax−b ∈ CY, x∈Cx, to the more general nonconic format: z* :=minx ctx,(GPd) s.t. Ax−b ∈ CY, x ∈P, where P is any closed convex set, not necessarily a cone, which we call the ground-set. Although any convex problem can be transformed to conic form, such transformations are neither unique nor natural given the natural description of many problems, thereby diminishing the relevance of data-based condition number theory. Herein we extend the modern theory of condition numbers to the problem format (GPd). As a byproduct, we are able to state and prove natural extensions of many theorems from the conic-based theory of condition numbers to this broader problem format.
