Steering Exact Penalty DCA for Nonsmooth DC Optimisation Problems with Equality and Inequality Constraints

We propose and study a version of the DCA (Difference-of-Convex functions Algorithm) using the $\ell_1$ penalty function for solving nonsmooth DC optimization problems with nonsmooth DC equality and inequality constraints. The method employs an adaptive penalty updating strategy to improve its performance. This strategy is based on the so-called steering exact penalty methodology and relies on solving some auxiliary convex subproblems to determine a suitable value of the penalty parameter. We present a detailed convergence analysis of the method and illustrate its practical performance by applying the method to two nonsmooth discrete optimal control problem.