The classical perceptron algorithm is an elementary row-action/relaxation algorithm for solving a homogeneous linear inequality system Ax 0. A natural condition measure associated with this algorithm is the Euclidean width T of the cone of feasible solutions, and the iteration complexity of the...

The classical perceptron algorithm is an elementary row-action/relaxation algorithm for solving a homogeneous linear inequality system Ax 0. A natural condition measure associated with this algorithm is the Euclidean width T of the cone of feasible solutions, and the iteration complexity of the...

We present a general theory for transforming a homogeneous conic system F: Ax = 0, x in C, x non-zero, to an equivalent system via projective transformation induced by the choice of a point in a related dual set. Such a projective transformation serves to pre-condition the conic system into a...

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,...

Given a convex body S and a point x in S, let sym(x,S) denote the symmetry value of x in S: sym(x,S):= max{t : x + t(x - y) is in S for every y in S}, which essentially measures how symmetric S is about the point x, and define sym(S):=max{sym(x,S) : x in S}. We call x* a symmetry point of S if...

We consider median regression and, more generally, quantile regression in high-dimensional sparse models. In these models the overall number of regressors p is very large, possibly larger than the sample size n, but only s of these regressors have non-zero impact on the conditional quantile of...