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* adding both ex9 sparse and ex9 sparse raja examples

* recasted TripletSparseMat and VectorPar to parent classes

Co-authored-by: Frank Wang <>
Co-authored-by: Cosmin G. Petra <>

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HiOp - HPC solver for optimization


HiOp is an optimization solver for solving certain mathematical optimization problems expressed as nonlinear programming problems. HiOp is a lightweight HPC solver that leverages application's existing data parallelism to parallelize the optimization iterations by using specialized linear algebra kernels.

Build/install instructions

HiOp uses a CMake-based build system. A standard build can be done by invoking in the 'build' directory the following

$> cmake ..
$> make 
$> make test
$> make install

This sequence will build HiOp, run integrity and correctness tests, and install the headers and the library in the directory '_dist-default-build' in HiOp's root directory.

Command make test runs extensive tests of the various modules of HiOp to check integrity and correctness. The tests suite range from unit testing to solving concrete optimization problems and checking the performance of HiOp solvers on these problems against known solutions. By default make test runs mpirun locally, which may not work on some HPC machines. For these HiOp allows using bsub to schedule make test on the compute nodes; to enable this, the use should use -DHIOP_TEST_WITH_BSUB=ON with cmake when building and run make test in a bsub shell session, for example,

bsub -P your_proj_name -nnodes 1 -W 30
make test

The installation can be customized using the standard CMake options. For example, one can provide an alternative installation directory for HiOp by using

$> cmake -DCMAKE_INSTALL_PREFIX=/usr/lib/hiop ..'

Selected HiOp-specific build options

  • Enable/disable MPI: -DHIOP_USE_MPI=[ON/OFF] (by default ON)
  • GPU support: -DHIOP_USE_GPU=ON. MPI can be either off or on. For more build system options related to GPUs, see "Dependencies" section below.
  • Enable/disable "developer mode" build that enforces more restrictive compiler rules and guidelines: -DHIOP_DEVELOPER_MODE=ON. This option is by default off.
  • Additional checks and self-diagnostics inside HiOp meant to detect abnormalities and help to detect bugs and/or troubleshoot problematic instances: -DHIOP_DEEPCHECKS=[ON/OFF] (by default ON). Disabling HIOP_DEEPCHECKS usually provides 30-40% execution speedup in HiOp. For full strength, it is recommended to use HIOP_DEEPCHECKS with debug builds. With non-debug builds, in particular the ones that disable the assert macro, HIOP_DEEPCHECKS does not perform all checks and, thus, may overlook potential issues.

For example:

$> make 
$> make test
$> make install

Other useful options to use with CMake

  • -DCMAKE_BUILD_TYPE=Release will build the code with the optimization flags on
  • -DCMAKE_CXX_FLAGS="-O3" will enable a high level of compiler code optimization


HiOp requires LAPACK and BLAS. These dependencies are automatically detected by the build system. MPI is optional and by default enabled. To disable use cmake option '-DHIOP_USE_MPI=OFF'.

HiOp has some support for NVIDIA GPU-based computations via CUDA and Magma. To enable the use of GPUs, use cmake with '-DHIOP_USE_GPU=ON'. The build system will automatically search for CUDA Toolkit. For non-standard CUDA Toolkit installations, use '-DHIOP_CUDA_LIB_DIR=/path' and '-DHIOP_CUDA_INCLUDE_DIR=/path'. For "very" non-standard CUDA Toolkit installations, one can specify the directory of cuBlas libraries as well with '-DHIOP_CUBLAS_LIB_DIR=/path'.

Using RAJA and Umpire portability libraries

Portability libraries allow running HiOp's linear algebra either on host (CPU) or a device (GPU). RAJA and Umpire are disabled by default. You can turn them on together by passing -DHIOP_USE_RAJA=ON to CMake. If the two libraries are not automatically found, specify their installation directories like this:

$> cmake -DHIOP_USE_RAJA=ON -DRAJA_DIR=/path/to/raja/dir -Dumpire_DIR=/path/to/umpire/dir

If the GPU support is enabled, RAJA will run all HiOp linear algebra kernels on GPU, otherwise RAJA will run the kernels on CPU using an OpenMP execution policy.

Support for GPU computations

When GPU support is on, HiOp requires Magma linear solver library and CUDA Toolkit. Both are detected automatically in most cases. The typical cmake command to enable GPU support in HiOp is

$> cmake -DHIOP_USE_GPU=ON ..

When Magma is not detected, one can specify its location by passing -DHIOP_MAGMA_DIR=/path/to/magma/dir to cmake.

For custom CUDA Toolkit installations, the locations to the (missing/not found) CUDA libraries can be specified to cmake via -DNAME=/path/cuda/directory/lib, where NAME can be any of


Below is an example for specifiying cuBlas, cuBlasLt, and nvblas libraries, which were NOT_FOUND because of a non-standard CUDA Toolkit instalation:

$> cmake -DHIOP_USE_GPU=ON -DCUDA_cublas_LIBRARY=/usr/local/cuda-10.2/targets/x86_64-linux/lib/lib64 -DCUDA_cublasLt_LIBRARY=/export/home/petra1/work/installs/cuda10.2.89/targets/x86_64-linux/lib/ -DCUDA_nvblas_LIBRARY=/export/home/petra1/work/installs/cuda10.2.89/targets/x86_64-linux/lib/ .. && make -j && make install

A detailed example on how to compile HiOp straight of the box on is available here.

RAJA and UMPIRE dependencies are usually detected by HiOp's cmake build system.

Kron reduction

Kron reduction functionality of HiOp is disabled by default. One can enable it by using

$> rm -rf *; cmake -DHIOP_WITH_KRON_REDUCTION=ON -DUMFPACK_DIR=/Users/petra1/work/installs/SuiteSparse-5.7.1 -DMETIS_DIR=/Users/petra1/work/installs/metis-4.0.3 .. && make -j && make install

Metis is usually detected automatically and needs not be specified under normal circumstances.

UMFPACK (part of SuiteSparse) and METIS need to be provided as shown above.

Interfacing with HiOp

HiOp supports three types of optimization problems, each with a separate input formats in the form of the C++ interfaces hiopInterfaceDenseConstraints,hiopInterfaceSparse and hiopInterfaceMDS. These interfaces are specified in hiopInterface.hpp and documented and discussed as well in the user manual.

hiopInterfaceDenseConstraints interface supports NLPs with billions of variables with and without bounds but only limited number (<100) of general, equality and inequality constraints. The underlying algorithm is a limited-memory quasi-Newton interior-point method and generally scales well computationally (but it may not algorithmically) on thousands of cores. This interface uses MPI for parallelization

hiopInterfaceSparse interface supports general sparse and large-scale NLPs. This functionality is similar to that of the state-of-the-art Ipopt (without being as robust and flexible as Ipopt is). Acceleration for this class of problems can be achieved via OpenMP or CUDA, however, this is work in progress and you are encouraged to contact HiOp's developers for up-to-date information.

hiopInterfaceMDS interface supports mixed dense-sparse NLPs and achives parallelization using GPUs and RAJA portability abstraction layer.

More information on the HiOp interfaces are here.

Running HiOp tests and applications

HiOp is using NVBlas library when built with CUDA support. If you don't specify location of the nvblas.conf configuration file, you may get an annoying warnings. HiOp provides default nvblas.conf file and installs it at the same location as HiOp libraries. To use it, set environment variable as

$ export NVBLAS_CONFIG_FILE=<hiop install dir>/lib/nvblas.conf

or, if you are using C-shell, as

$ setenv NVBLAS_CONFIG_FILE <hiop install dir>/lib/nvblas.conf

Existing issues

Users are highly encouraged to report any issues they found from using HiOp. One known issue is that there is some minor inconsistence between HiOp and linear package STRUMPACK. When STRUMPACK is compiled with MPI (and Scalapack), user must set flag HIOP_USE_MPI to ON when compiling HiOp. Otherwise HiOp won't load MPI module and will return an error when links to STRUMPACK, since the later one requires a valid MPI module. Similarly, if both Magma and STRUMPACK are linked to HiOp, user must guarantee the all the packages are compiled by the same CUDA compiler. User can check other issues and their existing status from


HiOp has been developed under the financial support of:

  • Department of Energy, Office of Advanced Scientific Computing Research (ASCR): Exascale Computing Program (ECP) and Applied Math Program.
  • Department of Energy, Advanced Research Projects Agency-Energy (ARPA‑E)
  • Lawrence Livermore National Laboratory, through the LDRD program


HiOp is written by Cosmin G. Petra ( and Nai-Yuan Chiang ( from LLNL and has received contributions from Slaven Peles (PNNL), Asher Mancinelli (PNNL), Cameron Rutherford (PNNL), Jake K. Ryan (PNNL), and Michel Schanen (ANL).


Copyright (c) 2017-2021, Lawrence Livermore National Security, LLC. All rights reserved. Produced at the Lawrence Livermore National Laboratory. LLNL-CODE-742473. HiOp is free software; you can modify it and/or redistribute it under the terms of the BSD 3-clause license. See COPYRIGHT and LICENSE for complete copyright and license information.