Nonsmooth Composite Optimization

Nonsmooth composite optimization focuses on solving optimization problems where the objective function is a sum of a smooth and a nonsmooth term, a common structure in many machine learning and signal processing applications. Current research emphasizes developing efficient algorithms, such as accelerated splitting methods, iteratively reweighted second-order methods, and block coordinate descent approaches, often tailored to specific problem structures like orthogonality constraints or sparsity-promoting regularizations. These advancements aim to improve convergence rates and computational efficiency, particularly for large-scale problems, impacting fields like statistical learning and deep neural network training.