An Algorithm for Nonsmooth Convex Minimization With Errors

A readily implementable algorithm is given for minimizing any convex, not necessarily differentiable, function/of several variables. At each iteration the method requires only one approximate evaluation of /and its E-subgradient, and finds a search direction by solving a small quadratic programming problem. The algorithm generates a minimizing sequence of points, which converges to a solution whenever/has any minimizers.