Partial Smoothness and Constant Rank
Adrian S. Lewis, Jingwei Liang, Tonghua Tian · SIAM Journal on Optimization · 2022
In optimization, the notion of a partly smooth objective function is powerful for applications in algorithmic convergence and postoptimality analysis, and yet is complex to define. A shift in focus to the first-order optimality conditions reduces the concept to a simple constant-rank condition. In this view, partial smoothness extends to more general variational systems, encompassing in particular the saddlepoint operators underlying popular primal-dual splitting algorithms. For a broad class of semi-algebraic generalized equations, partial smoothness holds generically.