Mesh processing tasks in computer graphics, including deformation and parameterization, are often cast as nonlinear minimization problems of the general form: min x f (x)(1)

Active research effort is dedicated to develop numerical optimization methods for the solution of such problems, taking advantage of the known context, eg, the geometric structure of the problem. Existing optimization algorithms typically produce a sequence of approximations, xn, designed to converge to a solution of (1). To this end, most approaches use, either explicitly or implicitly, a local quadratic approximation of the objective function: they construct an osculating convex quadric to f at xn, whose minimization determines the next approximation xn+ 1. From this point of view, the