On Smoothing Exact Penalty Functions for Convex Constrained Optimization

A quadratic smoothing approximation to nondifferentiable exact penalty functions for convex constrained optimization is proposed and its properties are established. The smoothing approximation is used as the basis of an algorithm for solving problems with (i) embedded network structures, and (ii) nonlinear minimax problems. Extensive numerical results with large-scale problems illustrate the efficiency of this approach.