The goal of this paper is to develop some computational experience and test the practical relevance of the theory of condition numbers C(d) for linear optimization, as applied to problem instances that one might encounter in practice. We used the NETLIB suite of linear optimization problems as a...

Our concern lies in solving the following convex optimization problem: minimize cx subject to Ax=b, x \in P, where P is a closed convex set. We bound the complexity of computing an almost-optimal solution of this problem in terms of natural geometry-based measures of the feasible region and the...

For a conic linear system of the form Ax ∈ K, K a convex cone, several condition measures have been extensively studied in the last dozen years. Among these, Renegar's condition number C(A) is arguably the most prominent for its relation to data perturbation, error bounds, problem geometry,...

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 E-optimal solutions, and...

The purpose of this paper is to extend, as much as possible, the modern theory of condition numbers for conic convex optimization: z_* = min cx subject to Ax-b \in C_Y , x \in C_X, to the more general non-conic format: (GP_d) z_* = min cx subject to Ax-b \in C_Y , x \in P, where P is any closed...

We present a practical algorithm for computing the minimum volume n-dimensional ellipsoid that must contain m given points a_1, ..., a_m \in R^n. This convex constrained problem arises in a variety of applied computational settings, particularly in data mining and robust statistics. Its...