MPCCModels.jl documentation

This package provides general guidelines to represent Mathematical Programs with Complementarity Constraints (MPCC) problems in Julia and a standardized API to evaluate the functions and their derivatives. The main objective is to be able to rely on that API when designing specialized MPCC solvers in Julia.

Introduction

This package is built for modelling problems of the form

\[\begin{aligned} \min \quad & f(x) \\ & \ell^c \le c(x) \le u^c,\\ & \ell^G\le G(x) \perp H(x)\ge \ell^H, \\ & \ell \leq x \leq u, \end{aligned}\]

where $f:\mathbb{R}^n\rightarrow\mathbb{R}$, $c:\mathbb{R}^n\rightarrow\mathbb{R}^m$, $G:\mathbb{R}^n\rightarrow\mathbb{R}^{n_{cc}}$, $H:\mathbb{R}^n\rightarrow\mathbb{R}^{n_{cc}}$, and $\ell_a \le a\perp b \ge \ell_b$ means that for each element of the vectors a and b, at least one must be zero.

Optimization problems are represented by an instance/subtype of AbstractMPCCModel. Such instances are composed of

an instance of MPCCModelMeta, which provides information about the problem, including the number of variables, constraints, bounds on the variables, etc. This MPCCModelMeta wraps an AbstractNLPModelMeta and only updates the necessary fields by overloading the getter api in NLPModels.jl.
the underlying AbstractNLPModel which stores the data necessary to build the MPCC.

Install

Install MPCCModels.jl with the following command.

pkg> add MPCCModels

This will enable the use of the API and the tools described here, and it allows the creation of a manually written model.

License

This content is released under the MIT License.