joint work with Jun-ya Gotoh, Katsuya Tono
We address the minimization of a smooth objective function under an L0-norm constraint and simple constraints. Some efficient algorithms are available when the problem has no constraints except the L0-norm constraint, but they often become inefficient when the problem has additional constraints. We reformulate the problem by employing a new DC (difference of two convex functions) representation of the L0-norm constraint, so that DC algorithm can retain the efficiency by boiling down its subproblems to the projection operation onto a simple set.
joint work with Min Tao
We consider the linear convergence of algorithms for structured DC optimization. We allow nonsmoothness in both of the convex and concave components, with a finite max structure in the concave component, and focus on algorithms computing d(irectional)-stationary points. Our results are based on standard error bounds assumptions and a new locally linear regularity regarding the intersection of certain stationary sets and dominance regions. A by-product of our work is a unified description of strong stationary points and global optimum by using the notion of approximate subdifferential.