Add Complementarity support for NL Writer v2

[quantresearch1]

Fixes # .

Summary/Motivation:

At work, I tried to use pyomo to solve a complementarity problem but it raised a ValueError as pyomo\repn\plugins\nl_writer.py does not know how to process Complementarity constraints.

Changes proposed in this PR:

-Add a block to handle complementarity constraints and the auxiliary variable/additional constraints after conversion to its standard form. When comparing my .nl file to AMPL's nl file, it seems that the additional equality constraint we add in to_standard_form() from complementarity.py is
c: (v - expression == 0)
while AMPL defines it as c:( v + expression == 0)
Essentially, Pyomo's auxiliary variable v is minus the auxiliary variable from AMPL, which makes it tricky to reconcile a .nl file written by Pyomo and one written by AMPL. I have not changed complementarity.py as Pyomo's choice is valid, it's simply a matter of convention.

Minimal example reproducing the issue being fixed:

from pyomo.environ import *
from pyomo.mpec import *
from pyomo.opt import WriterFactory
m = ConcreteModel()
m.x = Var(bounds=(0, 1))
m.y = Var(bounds=(0, 1))

m.c = Complementarity(expr=complements(m.x >= 0, m.y >= 0))
m.obj = Objective(expr=m.x+m.y, sense=maximize)
writer = WriterFactory('nl_v2')
filename_v2 = "model_v2.nl"
writer(m, filename_v2, solver_capability=(lambda x: False), io_options={})

Any ideas on how to test the validity of this implementation? I can see the .nl written by the code above has the correct number of variables (x, y and v the auxiliary), 2 constraints, one complementarity linear (5 1 3) and one equality (4 0)

g3 1 1 0 # problem unknown
3 2 1 0 1 # vars, constraints, objectives, ranges, eqns
0 0 1 0 0 0 # nonlinear constrs, objs; ccons: lin, nonlin, nd, nzlb
0 0 # network constraints: nonlinear, linear
0 0 0 # nonlinear vars in constraints, objectives, both
0 0 0 1 # linear network variables; functions; arith, flags
0 0 0 0 0 # discrete variables: binary, integer, nonlinear (b,c,o)
3 2 # nonzeros in Jacobian, obj. gradient
0 0 # max name lengths: constraints, variables
0 0 0 0 0 # common exprs: b,c,o,c1,o1
C0
n0
C1
n0
O0 1
n0
x0
r
5 1 3
4 0
b
0 0 1
0 0 1
2 0
k2
1
2
J0 1
1 1
J1 2
0 -1
2 1
G0 2
0 1
1 1

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[quantresearch1]

Hello, I was looking into the unit test failures, specifically the one named t11 in CCTests_nl_nlxfrm.
Looking at t11_nlxfrm.nl, I see the baseline has a linear complementarity constraint in its header while my output does not.
g3 1 1 0 # problem unknown
3 1 0 0 1 # vars, constraints, objectives, ranges, eqns; KNOWN BUG WITH NLv1 WRTIER!!!
0 0 1 0 0 0 # nonlinear constrs, objs; ccons: lin, nonlin, nd, nzlb

Looking into mpec4.py, I would have expected that no Complementarity component remain after the transformation due to the reclassify_component_type call, should that not the case?

    for cobj in instance.component_objects(
        Complementarity,
        active=True,
        descend_into=(Block, Disjunct),
        sort=SortComponents.deterministic,
    ):
        cobjs.append(cobj)
        for index in sorted(cobj.keys()):
            _cdata = cobj[index]
            if not _cdata.active:
                continue
            #
            # Apply a variant of the standard form logic
            #
            self.to_common_form(_cdata, free_vars)
            #
    tdata = instance._transformation_data['mpec.nl']
    tdata.compl_cuids = []
    for cobj in cobjs:
        tdata.compl_cuids.append(ComponentUID(cobj))
        cobj.parent_block().reclassify_component_type(cobj, Block)

[quantresearch1]

This is now done in the complementarity handling bit above

[quantresearch1]

I see that the _complementarity attribute is currently used below for the 'r' lines writing bit.
complementarity is mainly used in mpec4.py and ampl.py while _complementarity is used in complementarity.py and mpec1.py. Are they not the same ? If they are the same, I am happy to raise a separate PR to rename one into the other