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We tackle highly nonconvex, nonsmooth composite optimization problems whoseobjectives comprise a Moreau-Yosida regularized term. Classical nonconvexproximal splitting algorithms, such as nonconvex ADMM, suffer from lack ofconvergence for such a problem class. To overcome this difficulty, in this workwe consider a lifted variant of the Moreau-Yosida regularized model and proposea novel multiblock primal-dual algorithm that intrinsically stabilizes the dualblock. We provide a complete convergence analysis of our algorithm and identifyrespective optimality qualifications under which stationarity of the originalmodel is retrieved at convergence. Numerically, we demonstrate the relevance ofMoreau-Yosida regularized models and the efficiency of our algorithm on robustregression as well as joint feature selection and semi-supervised learning.

A Nonconvex Proximal Splitting Algorithm under Moreau-Yosida Regularization