The authors consider the problem of finding a set of points and/or weights which minimizes the condition number of the Gram matrix, \(k(A(x))\), defined by a polynomial basis. They propose a smoothing function for \(k(A(x))\) and show various properties of the smoothing function which ensure that a class of smoothing algorithms for solving the \(k(A(x))\) minimization problem converges to a Clarke stationary point globally.