MP2NL#

MP2NL translates MP-compatible syntax and features to any AMPL solver: the expressions described in the MP Modeling Guide (logical and counting constraints, piecewise-linear terms, complementarity, …) are reformulated into the solver’s native model type, for example a smooth nonlinear model for Ipopt or a model with integer variables for an MINLP solver. While this might mostly benefit MINLP solvers, such as Knitro or Couenne, NLP solvers (such as Ipopt) could benefit from automatic reformulation of complementarity constraints or (convex) piecewise-linear expressions.

Invocation#

Some of the nonlinear AMPL solvers (currently Knitro, BARON, CONOPT, LINDO Global), as well as the legacy solvers gurobiasl, cplexasl, xpressasl include the bridge and support option mp2nl=1. For any other AMPL solver, call mp2nl as the solver and name the real solver (the subsolver) inside it:

# a driver with the bridge built in
ampl.solve(solver="knitro", knitro_options="mp2nl=1 outlev=1")

# any other NL solver: MP2NL is the solver, the subsolver is named inside
ampl.solve(solver="mp2nl",
           mp2nl_options="solver=ipopt cvt:compl=2 cvt:compl:eps=1e-8 lim:time=60",
           ipopt_options="print_level=0")

ampl: option knitro_options 'mp2nl=1 outlev=1';
ampl: option solver knitro; solve;

ampl: option solver mp2nl;
ampl: option mp2nl_options 'solver=ipopt cvt:compl=2 cvt:compl:eps=1e-8 lim:time=60';
ampl: option ipopt_options 'print_level=0';
ampl: solve;

Enable the bridge whenever the model uses MP’s expressions, including the ==> syntax of indicator constraints: a solver that does not understand such a construct may misread the model without an error message.

Where the options go#

  • mp2nl_options: MP’s options. solver=, cvt:... (reformulations), acc:... (what the subsolver accepts), sol:chk:... (solution check), and generic ones such as lim:time, mip:gap, outlev. lim:time and mip:gap are passed on as the subsolver’s own keywords where MP2NL knows them.

  • <subsolver>_options: the subsolver’s own keywords. MP keywords placed here are usually rejected by the subsolver, and the solve fails.

  • With a built-in bridge (mp2nl=1), pass MP’s cvt:... and sol:chk:... options through the AMPL option mp_options.

Choosing the subsolver#

MP reformulates logic with binary variables, so the subsolver must accept the problem class after reformulation (outlev=1 prints the model before and after). A continuous NLP subsolver relaxes those binaries and can report an optimal solution that violates the logic; MP’s automatic solution check then prints “Tolerance violations”. Use an MINLP solver for models with logic; complementarity constraints alone, with a smooth reformulation (cvt:compl=1 or 2), can go to an NLP solver.

The status is the subsolver’s: a local solver’s “optimal” on a nonconvex model is a local optimum.

More: the MP documentation section Meta-driver MP2NL (configurations, printconfigs, config=, stub=, complementarity reformulations), and the notebooks tagged mp2nl.

Features#

Instrumentation#

For a generic summary of the options and features used most often, see Important features in the MP documentation.

The features below are handled by MP2NL itself; others depend on the subsolver and its options.

For all models

Multiple objectives

Emulated by MP. Option obj:multi. Details

Warm start

Option alg:start. Details

Solver options#

Full list of solver options:

Retrieving solutions#

The outcome of the last optimization is stored in the AMPL parameter solve_result_num and the relative message in solve_result.

display solve_result_num, solve_result;

MP2NL solve result codes can be obtained by running mp2nl -! or ampl: shell "mp2nl -!";:

Solve result table for MP2NL 0.2
          0- 99 solved: optimal for an optimization problem,
                feasible for a satisfaction problem 
        100-199 solved? solution candidate returned but error likely 
            150 solved? MP solution check failed (option sol:chk:fail) 
        200-299 infeasible 
        300-349 unbounded, feasible solution returned 
        350-399 unbounded, no feasible solution returned 
        400-449 limit, feasible: stopped, e.g., on iterations or Ctrl-C 
        450-469 limit, problem is either infeasible or unbounded.
                Disable dual reductions or run IIS finder for definitive answer.
        470-499 limit, no solution returned 
        500-999 failure, no solution returned 
            550 failure: numeric issue, no feasible solution

For general information, see MP result codes guide.

Changelog#