Complementarity.jl

Provides a modeling interface for mixed complementarity problems (MCP) and math programs with equilibrium problems (MPEC) via JuMP
Popularity
75 Stars
Updated Last
10 Months Ago
Started In
April 2016

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: Differences between PATHSolver.jl and Complementarity.jl:

  • PATHSolver.jl provides a wrapper for the C API of the PATH solver.
  • PATHSolver.jl also enables JuMP for solving MCP, but limited to linear problems.
  • Complementarity.jl provides a JuMP extension for solving MCP, both linear and nonlinear, using the C API wrapper in PATHSolver.jl.

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(Ipopt.Optimizer)
@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.

Used By Packages

No packages found.