Quadratic approximations in convex nondifferentiable optimization

An implementable descent method for the unconstrained minimization of convex nonsmooth functions of several variables is described. The algorithm is characterized by the use of a set of quadratic approximations of the objective function in order to compute the search direction. The resulting direction finding subproblem is shown to be equivalent to a structured parametric quadratic programming problem. The convergence of the algorithm to the minimum is proved, and numerical experience is reported.