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

Steering exact penalty DCA for nonsmooth DC optimization problems with equality and inequality constraints