The following configuration successfully builds and runs the package:

Compiler:
    GCC 8.2.0 (also MinGW-w64 based on this GCC)
    LLVM/clang 3.7.1
    Intel C++ Composer XE 19.0

Third-party libraries:
    GSL 2.3
    OpenBLAS 0.3.4
    UMFPACK 5.7.1           (part of SuiteSparse 5.4.0)
    sqlitepp 0.2            (included in libs/, works e.g. with sqlite3 3.15.0)
    CLN 1.3.4
    GiNaC 1.6.4

MPI (optional)
    OpenMPI 4.0.0
    Microsoft MPI v6

Other optional dependencies:
    png++ 0.2.5             (included in libs/, works e.g. with libpng 1.6.6)
    OpenCL 2.0              (but e.g. AMD HD7970 works all right, even though is officially supports only OpenCL 1.1)
    SuperLU 5.0             (not recommended due to high memory requirements)
    MUMPS 5.1.2             (older versions seem to fail OOC mode)
    Pardiso 5.0.0           (or the MKL Pardiso)

Code documentation generation:
    Doxygen 1.8.5