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HiOp supports three input formats: hiopInterfaceDenseConstraints,hiopInterfaceSparse and hiopInterfaceMDS. All formats are in the form of C++ interfaces (e.g., abstract classes), see hiopInterface.hpp file, that the user must instantiate/implement and provide to HiOp.

Please read carefully the (software) documentation provided in hiopInterface.hpp and the (math) documentation provided in the user manual. In addition, please be aware of the following notes in the case of hiopInterfaceSpare or hiopInterfaceMDS.

Key points/conventions for hiopInterfaceSparse

Jacobian and Hessian

  • both Jacobian and Hessian are sparse, and their triplet forms are user inputs via the interface.
  • Jacobian is implemented as a general sparse matrix and hence user need to provide all the nonzeros of it.
  • Hessian is implemented as a symmetric sparse matrix and hence user only need to provide a triangular part of it.
  • for conventions on symmetric matrices and sparse matrices see this

Key points/conventions for hiopInterfaceMDS

MDS stands for mixed dense-sparse, meaning that the derivatives (Jacobian and Hessian) have both dense and sparse blocks. The hiopInterfaceMDS allows the user to pass these blocks to HiOp, which then exploits this structure using a specialized linear algebra implementation. This feature is especially relevant for GPU (hybrid) computing mode.

Optimization variables

  • the (vector of) optimization variables are supposed to be split in dense and sparse variables
  • HiOp expects the optimization variables in a certain order: sparse variables first, followed by dense variables
    • the implementer/user (inconveniently) has to keep an map between his internal variables indexes and the indexes HiOp expects in order to avoid expensive memory moves inside HiOp

Jacobian

  • the columns in the Jacobian corresponding to sparse variables form the sparse Jacobian block (and can/should be provided as a sparse matrix, see eval_Jac function(s))
  • the columns in the Jacobian corresponding to dense variables form the dense Jacobian block (and can/should be provided via the double** buffer provided by eval_Jac functions(); this buffer is primed to support double indexing, i.e., use buffer[i][j] to access the (i,j) element of the dense block)
  • as indicated at the previous bullet, the user needs to map the column/variable index in the true Jacobian to the column index in the sparse or dense Jacobian block. The indexes inside the sparse and dense Jacobian blocks is zero-based

Hessian

  • the Hessian's structure is slightly different that of the Jacobian. The Hessian has three relevant blocks
    • Hessian with respect to (sparse,sparse) variables
    • Hessian with respect to (dense,dense) variables
    • Hessian with respect to (sparse,dense) variables, which is the transpose of (dense,sparse) Hessian. This blocks are ignored currently by HiOp (subject to change)
  • all the above indexing rules for the Jacobian blocks apply to the Hessian blocks
  • for conventions on symmetric matrices and sparse matrices see this