Reference

AmplMPECModel

Smooth reformulation for an Ampl model with complementarity constraints.

The nonlinear program

\[\begin{aligned} min_x \quad & f(x)\\ \mathrm{s.t.} \quad & c_L ≤ c(x) ≤ c_U,\\ & g_L ≤ g(x) ⟂ x ≥ x_L, \end{aligned}\]

is reformulated as

\[\begin{aligned} min_x \quad & f(x)\\ \mathrm{s.t.} \quad &  c_L ≤ c(x) ≤ c_U,\\ & g_L ≤ g(x) \\ & x_L ≤ x \\ & Diag(g(x)) x ≤ 0 \end{aligned}\]

Return the original model if it does not have complementarity constraints.

AmplNLPMeta <: AbstractNLPModelMeta

A composite type that represents the main features of the optimization problem

optimize    obj(x)
subject to  lvar ≤    x    ≤ uvar
            lcon ≤ cons(x) ≤ ucon

where x is an nvar-dimensional vector, obj is the real-valued objective function, cons is the vector-valued constraint function, optimize is either "minimize" or "maximize".

Here, lvar, uvar, lcon and ucon are vectors. Some of their components may be infinite to indicate that the corresponding bound or general constraint is not present.

AmplNLPMeta(nvar; kwargs...)

Create an AmplNLPMeta with nvar variables. The following keyword arguments are accepted:

• x0: initial guess
• lvar: vector of lower bounds
• uvar: vector of upper bounds
• nbv: number of linear binary variables
• niv: number of linear non-binary integer variables
• nlvb: number of nonlinear variables in both objectives and constraints
• nlvo: number of nonlinear variables in objectives (includes nlvb)
• nlvc: number of nonlinear variables in constraints (includes nlvb)
• nlvbi: number of integer nonlinear variables in both objectives and constraints
• nlvci: number of integer nonlinear variables in constraints only
• nlvoi: number of integer nonlinear variables in objectives only
• nwv: number of linear network (arc) variables
• ncon: number of general constraints
• y0: initial Lagrange multipliers
• lcon: vector of constraint lower bounds
• ucon: vector of constraint upper bounds
• nnzo: number of nonzeros in all objectives gradients
• nnzj: number of elements needed to store the nonzeros in the sparse Jacobian
• lin_nnzj: number of elements needed to store the nonzeros in the sparse Jacobian of linear constraints
• nln_nnzj: number of elements needed to store the nonzeros in the sparse Jacobian of nonlinear constraints
• nnzh: number of elements needed to store the nonzeros in the sparse Hessian
• nlin: number of linear constraints
• nnln: number of nonlinear general constraints
• nnnet: number of nonlinear network constraints
• nlnet: number of linear network constraints
• lin: indices of linear constraints
• nln: indices of nonlinear constraints
• nnet: indices of nonlinear network constraints
• lnet: indices of linear network constraints
• minimize: true if optimize == minimize
• nlo: number of nonlinear objectives
• islp: true if the problem is a linear program
• n_cc: number of complementarity constraints
• cvar: indices of variables appearing in complementarity constraints (0 if constraint is regular)
• name: problem name