Structure-aware methods for expensive derivative-free nonsmooth composite optimization
- We present new methods for solving a broad class of bound-constrained nonsmooth
composite minimization problems. These methods are specially designed for objec-
tives that are some known mapping of outputs from a computationally expensive
function. We provide accompanying implementations of these methods: in particular,
a novel manifold sampling algorithm (MS-P) with subproblems that are in a sense
primal versions of the dual problems solved by previous manifold sampling methods
and a method (GOOMBAH) that employs more difficult optimization subproblems. For
these two methods, we provide rigorous convergence analysis and guarantees. We
demonstrate extensive testing of these methods. Open-source implementations of the
methods developed in this manuscript can be found at https://github.com/POptUS/
IBCDFO/.
