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,...

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...