KKT systems

BieglerKKTSystem{T, VI, VT, MT, SMT} <: MadNLP.AbstractReducedKKTSystem{T, VT, MT}

Implementation of Biegler's reduction method [BNS2015] in MadNLP's syntax. The API follows the MadNLP's specifications. The reduction is at the basis of the linearize-then-reduce method described in [PSSMA2022].

Return a dense matrix that can be factorized efficiently inside MadNLP by any dense linear algebra routine (e.g. Lapack).

Examples

julia> flp = Argos.FullSpaceEvaluator("case9.m")

julia> opf = Argos.OPFModel(flp)

julia> T = Float64

julia> VI, VT, MT = Vector{Int}, Vector{T}, Matrix{T}

julia> kkt = Argos.BieglerKKTSystem{T, VI, VT, MT}(opf)

julia> MadNLP.get_kkt(kkt) # return the matrix to factorize

Notes

BieglerKKTSystem can be instantiated both on the host memory (CPU) or on a NVIDIA GPU using CUDA. When instantiated on the GPU, BieglerKKTSystem uses cusolverRF to streamline the solution of the sparse linear systems in the reduction algorithm.

References

[BNS2015] Biegler, Lorenz T., Jorge Nocedal, and Claudia Schmid. "A reduced Hessian method for large-scale constrained optimization." SIAM Journal on Optimization 5, no. 2 (1995): 314-347.

[PSSMA2022] Pacaud, François, Sungho Shin, Michel Schanen, Daniel Adrian Maldonado, and Mihai Anitescu. "Condensed interior-point methods: porting reduced-space approaches on GPU hardware." arXiv preprint arXiv:2203.11875 (2022).