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.
- This package provides a modeling and computational interface for solving Mixed Complementarity Problems (MCP): modeling by JuMP.jl and computing by PATHSolver.jl and NLsolve.jl. See the 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 getvalue(x)- For solving mathematical programs with equilibrium constraints (MPEC), this package provides an extension to JuMP.jl by providing a macro that accepts complementarity conditions as constraints. Then it reformulates the complementarity conditions as a set of equality and inequality constraints so that a nonlinear optimization solver such as Ipopt.jl can solve the problem. See the 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)Pkg.add("Complementarity")This will also install a few other packages.