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Complementarity.jl

Build Status codecov

This package provides modeling language for (1) mixed complementarity problems (MCP) and (2) mathematical programs with equilibrium problems (MPEC).

NOTE @complmentarity for MCP and @complements for MPEC.

Mixed Complementarity Problems (MCP)

NOTE: The PATHSolver.jl has been completely rewritten between v0.6.2 and v1.1.0. Now PATHSolver.jl provides both an interface to the PATH solver and an integration to JuMP, but only limited to linear problems at this moment. For nonlinear problems, you still need to use Complementarity.jl, which now also uses the new PATHSolver.jl as its solver. Most parts of Complementarity.jl remain the same, except how the solver options are passed.

MCP Documentation

F(x) ⟂ lb ≤ x ≤ ub

A very simple example:

(x+2) x = 0,  x ≥ 0,   x+2 ≥ 0
using Complementarity, JuMP
m = MCPModel()
@variable(m, x >= 0)
@mapping(m, F, x+2)
@complementarity(m, F, x)
status = solveMCP(m)
@show result_value(x)

Mathematical Programs with Equilibrium Constraints (MPEC)

NOTE: For solving MPEC, JuMP.jl v0.21 has started supporting complementarity constraints. At this moment, GAMS.jl and KNITRO support complementarity constraints.

MPEC Documentation

min  f(x)
s.t. g(x) ≤ 0
     F(x) ⟂ lb ≤ x ≤ ub

A very simple example:

min  x^3
s.t. (x+2) x = 0,  x ≥ 0,   x+2 ≥ 0
using JuMP, Ipopt, Complementarity
m = Model(solver=IpoptSolver())
@variable(m, x>=0)
@NLobjective(m, Min, x^3)
@complements(m, 0 <= x+2,   x >= 0)
solve(m)
@show getvalue(x)

Installation

Pkg.add("Complementarity")

This will also install a few other packages.