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...

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...

This paper studies the marketing problem of a firm trying to obtain an attractive mix of customers by making customized offers. The firm values the average features of the acquired set of customers, makes decisions with uncertainty about whether and which customers will accept offers, is risk...