Procedure GMP::SolverSession::AddLinearization(solverSession, GMP, solution, constraintSet, jacTol, local, purgeable)

GMP::SolverSession::AddLinearization

The procedure GMP::SolverSession::AddLinearization adds a linearization row to a solver session with respect to a solution (column level values and row marginals) of a generated mathematical program for each row in a set of nonlinear constraints of that generated mathematical program.

GMP::SolverSession::AddLinearization(
     solverSession,    ! (input) a solver session
     GMP,              ! (input) a generated mathematical program
     solution,         ! (input) a solution
     constraintSet,    ! (input) a set of nonlinear constraints
     [jacTol],         ! (optional) the Jacobian tolerance
     [local],          ! (optional, default 0) a scalar binary expression
     [purgeable]       ! (optional, default 0) a scalar binary expression
     )

Arguments

solverSession

An element in the set AllSolverSessions.

GMP

An element in AllGeneratedMathematicalPrograms.

solution

An integer scalar reference to a solution in the solution repository of GMP.

constraintSet

A subset of AllNonLinearConstraints.

jacTol

The Jacobian tolerance; if the Jacobian value (in absolute sense) of a column in a nonlinear row is smaller than this value, the column will not be added to the linearization of that row. The default is 1e-5.

local

A scalar binary value to indicate whether the linearization is valid for the local problem (i.e. the problem corresponding to the current node in the solution process and all its descendant nodes) only (value 1) or for the global problem (value 0).

purgeable

A scalar binary value to indicate whether the solver is allowed to purge the cut if it deems it ineffective. If the value is 1, then it is allowed.

Return Value

The procedure returns 1 on success, or 0 otherwise.

Note

  • This procedure fails if one of the constraints is ranged.

  • This procedure can only be called from within a CallbackAddCut or CallbackAddLazyConstraint callback procedure.

  • A CallbackAddCut callback procedure will only be called when solving mixed integer programs with CPLEX or Gurobi. In case of Gurobi the cuts are always local even if argument local has value 0.

  • A CallbackAddLazyConstraint callback procedure will only be called when solving mixed integer programs with CPLEX or Gurobi.

  • Argument purgeable can only be used with CPLEX. If the cut is local then the cut will not be purgeable even if argument purgeable has value 1.

  • This procedure will fail if GMP contains a column that is not part of the generated mathematical program corresponding to solverSession. A column that is part of GMP but not of the generated mathematical program corresponding to solverSession will be ignored, i.e., no coefficient for that column will be added to the linearizations.

  • The formula for the linearization of a scalar nonlinear inequality \(g(x,y) \leq b_j\) around the point \((x,y) = (x^0,y^0)\) is as follows.

    \[\begin{split}g(x^0,y^0) + \bigtriangledown g(x^0,y^0)^T \begin{bmatrix} x - x^0 \\ y - y^0 \end{bmatrix} \leq b_j\end{split}\]

See also

The routines GMP::Linearization::Add, GMP::Instance::SetCallbackAddCut, GMP::Instance::SetCallbackAddLazyConstraint and GMP::SolverSession::GenerateCut.