BARON Writer Outputs Inconsistent Constraint Expressions for Model with Fixed Var Objects

[shermanjasonaf]

Summary

For fixed reals $x, t, u_0, u_1$, consider the model

$$P(x, t, u_0, u_1):~~\begin{array}[t]{clll} \displaystyle \min_{d_0, d_1, z_{0}, z_{1} \geq 0} & \displaystyle d_0 + d_1 \\\ \mathrm{s.t.} & (x - 4)^2 + (z_{i} - 1)^2 - t \leq 0 \qquad & i = 0, 1 \quad & (\text{epigraph}) \\\ & z_{i} = d_0 + u_{i} d_{1} & i = 0, 1 \quad & (\text{DR}) \\\ & \sqrt{u}_{i}x - u_iz - 2 \leq 0 & i = 0, 1 \quad & (\text{Leyffer}) \end{array}$$

If $x$ is represented by a fixed Var object in the implementation of this model, instead of, say, an immutable Param object, then the *.bar file obtained via the BARON writer seems to contain an incorrect representation of the "epigraph" constraints. More precisely, instead of the original epigraph constraints

$$(x - 4)^2 + (z_{i} - 1)^2 - t \leq 0, \qquad i = 0, 1$$

the BARON writer output actually represents

$$-(x - 4)^2 + (z_{i} - 1)^2 - t \leq 0, \qquad i = 0, 1$$

Since the Pyomo BARON solver interface (solvers.plugins.solvers.BARON) relies on the Pyomo BARON writer, solving the Pyomo model with BARON may yield an incorrect result. This issue may also affect the PyROS solver (contrib.pyros), which makes extensive use of models with fixed Var objects, if BARON is passed as a subsolver.

Steps to reproduce the issue

Script for building, writing, and solving the Pyomo model with $x=3.5, t = 0.55, u_0 = 9/8, u_1 = 13/10$:

# example.py
import pyomo.environ as pyo


def create_model(x, t, u0, u1, make_x_fixed_var=True):
    """
    Create model.
    """
    m = pyo.ConcreteModel()

    if make_x_fixed_var:
        m.x = pyo.Var(initialize=x)
        m.x.fix()
    else:
        m.x = pyo.Param(initialize=x)

    m.u = pyo.Param(initialize=9/8)
    m.d0 = pyo.Var(bounds=(0, None))
    m.d1 = pyo.Var(bounds=(0, None))

    m.scenarios = pyo.Block(range(2))
    for u_val, blk in zip([u0, u1], m.scenarios.values()):
        blk.z = pyo.Var(bounds=(0, None))
        blk.u = pyo.Param(initialize=u_val)

        blk.epigraph_con = pyo.Constraint(
            expr=(m.x - 4) ** 2 + (blk.z - 1) ** 2 - t <= 0
        )
        blk.leyffer_con = pyo.Constraint(
            expr=pyo.sqrt(m.u) * m.x - blk.u * blk.z - 2 <= 0
        )
        blk.dr_con = pyo.Constraint(
            expr=blk.z == m.d0 + blk.u * m.d1
        )
    m.obj = pyo.Objective(expr=m.d0 + m.d1)

    return m


if __name__ == "__main__":
    for make_x_fixed_var in [True, False]:
        model = create_model(
            x=3.5,
            t=0.55,
            u0=9/8,
            u1=13/10,
            make_x_fixed_var=make_x_fixed_var,
        )
        model.write(
            f"model_with_fixed_var_{make_x_fixed_var}.bar",
            io_options={"symbolic_solver_labels": True},
        )
        solver = pyo.SolverFactory("baron")
        solver.solve(model)
        print(f"Solution with make_x_fixed_var={make_x_fixed_var}:")
        print(f"\tz0={pyo.value(model.scenarios[0].z)}")
        print(f"\tz1={pyo.value(model.scenarios[1].z)}")
        print(f"\td0={pyo.value(model.d0)}")
        print(f"\td1={pyo.value(model.d1)}")

Error Message

Console output. Remains the same across different BARON executables (22.11.03, 23.1.5, 23.2.27, 23.3.11)

$ python example.py
Solution with make_x_fixed_var=True:
        z0=1.5220538677594437
        z1=1.7588178025829206
        d0=0.0
        d1=1.3529367712253249
Solution with make_x_fixed_var=False:
        z0=1.5220538677594437
        z1=1.547722557316334
        d0=1.3570408625028816
        d1=0.14667822677957854

BARON writer output model_with_fixed_var_True.bar. Notice the epigraph constraints (represented in file by s_igraph_con_1_ and s_igraph_con_4_ are inconsistent with the original model epigraph constraints.

OPTIONS {
Summary: 0;
}

POSITIVE_VARIABLES ONE_VAR_CONST__, d0, d1, scenarios_0__z, scenarios_1__z;

LOWER_BOUNDS{
d0: 0;
d1: 0;
scenarios_0__z: 0;
scenarios_1__z: 0;
}

EQUATIONS c_e_FIX_ONE_VAR_CONST__, s_igraph_con_1_, s_eyffer_con_2_, s__0__dr_con_3_, s_igraph_con_4_, s_eyffer_con_5_, s__1__dr_con_6_;

c_e_FIX_ONE_VAR_CONST__:  ONE_VAR_CONST__  == 1;
s_igraph_con_1_: -0.5 ^ 2 + (scenarios_0__z - 1) ^ 2 + (-0.55) <= 0;
s_eyffer_con_2_: 3.7123106012293743 + (-1.125)*scenarios_0__z - 2 <= 0;
s__0__dr_con_3_: scenarios_0__z - (d0 + 1.125*d1) == 0;
s_igraph_con_4_: -0.5 ^ 2 + (scenarios_1__z - 1) ^ 2 + (-0.55) <= 0;
s_eyffer_con_5_: 3.7123106012293743 + (-1.3)*scenarios_1__z - 2 <= 0;
s__1__dr_con_6_: scenarios_1__z - (d0 + 1.3*d1) == 0;

OBJ: minimize d0 + d1;

STARTING_POINT{
ONE_VAR_CONST__: 1;
}

BARON writer output: model_with_fixed_var_False.bar. Notice the epigraph constraints (represented in file by s_igraph_con_1_ and s_igraph_con_4_ are consistent with the original model epigraph constraints.

OPTIONS {
Summary: 0;
}

POSITIVE_VARIABLES ONE_VAR_CONST__, d0, d1, scenarios_0__z, scenarios_1__z;

LOWER_BOUNDS{
d0: 0;
d1: 0;
scenarios_0__z: 0;
scenarios_1__z: 0;
}

EQUATIONS c_e_FIX_ONE_VAR_CONST__, s_igraph_con_1_, s_eyffer_con_2_, s__0__dr_con_3_, s_igraph_con_4_, s_eyffer_con_5_, s__1__dr_con_6_;

c_e_FIX_ONE_VAR_CONST__:  ONE_VAR_CONST__  == 1;
s_igraph_con_1_: 0.25 + (scenarios_0__z - 1) ^ 2 + (-0.55) <= 0;
s_eyffer_con_2_: 3.7123106012293743 + (-1.125)*scenarios_0__z - 2 <= 0;
s__0__dr_con_3_: scenarios_0__z - (d0 + 1.125*d1) == 0;
s_igraph_con_4_: 0.25 + (scenarios_1__z - 1) ^ 2 + (-0.55) <= 0;
s_eyffer_con_5_: 3.7123106012293743 + (-1.3)*scenarios_1__z - 2 <= 0;
s__1__dr_con_6_: scenarios_1__z - (d0 + 1.3*d1) == 0;

OBJ: minimize d0 + d1;

STARTING_POINT{
ONE_VAR_CONST__: 1;
}

Information on your system

Pyomo version: 6.5.1dev0 #b2101fd
Python version: 3.9.13
Operating system: Ubuntu 20.04
How Pyomo was installed (PyPI, conda, source): source
Solver (if applicable): BARON

Additional information