ComplementaritySolve.jl

A package for solving complementarity problems in Julia with scalable gradients compatible with ChainRules.

Installation

import Pkg
Pkg.add("https://github.com:avik-pal/ComplementaritySolve.jl.git")

Implemented Problems & Algorithms

LCP Solvers

Solver	Native Batching	CPU	CUDA1	Details
NonlinearReformulation	✔️	✔️	✔️
RPGS	❌	✔️	❌
PGS	❌	✔️	❌
PSOR	❌	✔️	❌
BokhovenIterativeAlgorithm	✔️	✔️	✔️	Assumes PSD M
InteriorPointMethod	✔️	✔️	✔️	Assumes PSD M

Solvers that don't natively support batching, use threads to solve multiple problems in parallel.

MCP Solvers

Solver	CPU	CUDA1	Details
NonlinearReformulation	✔️	✔️
PATHSolver	✔️	❌	Provides an uniform API to access path.c Only Float64 is supported, all inputs will be cast to Float64.

All LCPs, MLCPs, and NCPs can be converted to MCPs, and these solvers can be used directly.

Adjoint Methods

Method	Problem Type	Native Batching	CPU	CUDA1	Details
LinearComplementarityAdjoint	LCP	✔️	✔️	✔️
MixedComplementarityAdjoint	MCP		✔️	✔️

Usage

More details are WIP. Examples can be found in test directory.

Current Unique Features of ComplementaritySolve.jl:

• Supports batched problems for LCPs.
• Can use any arbitrary forward solver. If Siconos is faster, we can use that solver, and we will still be able to give gradients to the end user.
• Most solvers should work on GPUs OOTB.
• Scalable Adjoint computation using Linear Solve trick rather than computing explicit Jacobians like ParametricMCPs.jl.
  • If solver thinks problem is small enough, we still construct the Jacobian.

Footnotes

1. Solvers internally using NonlinearSolve.jl need to use a CUDA compatible solver (like SimpleNewtonRaphson()). ↩ ↩² ↩³