MadNLP.jl: A Mad Nonlinear Programming Solver.

07/29/2021, 5:00 PM5:10 PM UTC
JuMP Track

Abstract:

We present a native-Julia nonlinear programming (NLP) solver MadNLP.jl. This solver implements the filter line-search interior-point method for constrained NLPs; to the best of our knowledge, MadNLP is currently the only native-Julia solver that is capable of handling general nonlinear equality/inequality-constrained optimization problems. MadNLP is interfaced with the algebraic modeling language JuMP.jl, the graph-based modeling language Plasmo.jl, and the NLP data structure NLPModels.jl.

Description:

MadNLP leverages diverse sparse and dense linear algebra routines: UMFPACK, HSL routines, MUMPS, Pardiso, LAPACK, and cuSOLVER. The key feature of MadNLP is the adoption of scalable linear algebra methods: structure-exploiting parallel linear algebra (based on restricted additive Schwarz and Schur complement strategy) and GPU-based linear algebra (cuSOLVER). These methods significantly enhance the scalability of the solver to large-scale problem instances (e.g., long-horizon dynamic optimization, stochastic programs, abd dense NLPs). Furthermore, MadNLP exploits Julia's extensibility so that new linear solvers can be added in a plug-and-play manner. In the presentation, we will present benchmark results against other open-source and commercial solvers as well as the results highlighting MadNLP's advanced features. Our results suggest that (i) MadNLP has comparable speed and robustness with Ipopt/KNITRO when tested against the standard benchmark test set (CUTEst); (ii) MadNLP with structure-exploiting parallel linear algebra can achieve speed-up up of a factor of 3 when solving large-scale sparse nonlinear programs; and (iii) GPU-acceleration achieves the speed-up of a factor of 10 when solving dense nonlinear optimization problems. The presentation will conclude with a future development roadmap, including the implementation of distributed-memory parallelism and pure-GPU solver.

Platinum sponsors

Julia Computing

Gold sponsors

Relational AI

Silver sponsors

Invenia LabsConningPumas AIQuEra Computing Inc.King Abdullah University of Science and TechnologyDataChef.coJeffrey Sarnoff

Media partners

Packt Publication

Fiscal Sponsor

NumFOCUS