  We present new methods for solving a broad class of bound-constrained
nonsmooth composite minimization problems. These methods are specially designed
for objectives 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 (\mspshortref) with
subproblems that are in a sense primal versions of the dual problems solved by
previous manifold sampling methods and a method (\goombahref) 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 \url{github.com/POptUS/IBCDFO/}.
