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https://github.com/chkwon/complementarity.jl
provides a modeling interface for mixed complementarity problems (MCP) and math programs with equilibrium problems (MPEC) via JuMP
https://github.com/chkwon/complementarity.jl
complementarity complementarity-conditions equilibrium equilibrium-constraints mathematical-programming mathematical-programs mcp optimization
Last synced: 26 days ago
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provides a modeling interface for mixed complementarity problems (MCP) and math programs with equilibrium problems (MPEC) via JuMP
- Host: GitHub
- URL: https://github.com/chkwon/complementarity.jl
- Owner: chkwon
- License: other
- Created: 2016-04-27T03:18:00.000Z (over 8 years ago)
- Default Branch: master
- Last Pushed: 2024-05-13T13:56:30.000Z (6 months ago)
- Last Synced: 2024-07-10T02:17:40.998Z (4 months ago)
- Topics: complementarity, complementarity-conditions, equilibrium, equilibrium-constraints, mathematical-programming, mathematical-programs, mcp, optimization
- Language: Julia
- Homepage:
- Size: 241 KB
- Stars: 75
- Watchers: 11
- Forks: 20
- Open Issues: 6
-
Metadata Files:
- Readme: README.md
- License: LICENSE.md
Awesome Lists containing this project
README
# Complementarity.jl
[](https://github.com/chkwon/Complementarity.jl/actions?query=workflow%3ACI)
[](https://codecov.io/gh/chkwon/Complementarity.jl)
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](https://github.com/chkwon/PATHSolver.jl) provides a wrapper for the C API of the [PATH](http://pages.cs.wisc.edu/~ferris/path.html) solver.
- [PATHSolver.jl](https://github.com/chkwon/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](MCP.md)***
- This package provides a modeling and computational interface for solving [Mixed Complementarity Problems](https://en.wikipedia.org/wiki/Mixed_complementarity_problem) (MCP): modeling by [JuMP.jl](https://github.com/JuliaOpt/JuMP.jl) and computing by [PATHSolver.jl](https://github.com/chkwon/PATHSolver.jl) and [NLsolve.jl](https://github.com/EconForge/NLsolve.jl). See [the documentation](MCP.md).
```
F(x) ⟂ lb ≤ x ≤ ub
```
A very simple example:
```
(x+2) x = 0, x ≥ 0, x+2 ≥ 0
```
```julia
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](http://www.juliaopt.org/JuMP.jl/v0.21.1/constraints/#Complementarity-constraints-1). At this moment, [GAMS.jl](https://github.com/GAMS-dev/gams.jl) and [KNITRO](https://github.com/jump-dev/KNITRO.jl) support complementarity constraints.
***[MPEC Documentation](MPEC.md)***
- For solving [mathematical programs with equilibrium constraints (MPEC)](https://en.wikipedia.org/wiki/Mathematical_programming_with_equilibrium_constraints), this package provides an extension to [JuMP.jl](https://github.com/JuliaOpt/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](https://github.com/JuliaOpt/Ipopt.jl) can solve the problem. See [the documentation](MPEC.md).
```
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
```
```julia
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
```julia
Pkg.add("Complementarity")
```
This will also install a few other packages.