ParametricMCPs

This packages provide a generic, differentiable mathematical programming layer by compiling mixed complementarity problems (MCPs) parameterized by a "runtime"-parameter vector. The resulting ParametricMCP can solved for different parameter instantiations using solve(problem, paramters) and the solve routine is made differentiable via ChainRulesCore.

Installation

This package is not yet registered. For now, simply install it as git dependency (and don't forget to check-in you Manifest.toml if you do).

] add https://github.com/lassepe/ParametricMCPs.jl

Quickstart by Example

Simple forward computation:

using ParametricMCPs

# setup a simple MCP which represents a QP with
# - cost: sum((z[1:2] - θ).^2)
# - constaints: z[1:2] >= 0

f(z, θ) = [2z[1:2] - z[3:4] - 2θ; z[1:2]]
lower_bounds = [-Inf, -Inf, 0, 0]
upper_bounds = [Inf, Inf, Inf, Inf]
problem = ParametricMCP(f, lower_bounds, upper_bounds, parameter_dimension)

some_parameter = [1.0, 2.0]
solve(problem, some_parameter)

Since we provide differentiation rules via ChainRulesCore, the solver can be using your favourite ad-framework, e.g., Zygote:

using Zygote

function dummy_pipeline(θ)
    solution = ParametricMCPs.solve(problem, θ)
    sum(solution.z .^ 2)
end

Zygote.gradient(dummy_pipeline, some_parameter)