GDPopt LOA reports non-rigorous nonconvex bounds as optimal LB=UB

Summary

GDPopt LOA can report TerminationCondition.optimal with problem.lower_bound == problem.upper_bound on nonconvex GDPs even when those bounds are not rigorous.

This is not a request for LOA to prove global optimality on nonconvex problems. Pyomo already documents that "For nonconvex problems, LOA may not report rigorous lower/upper bounds." The issue is that the returned SolverResults object still uses the unqualified global-looking fields:

results.solver.termination_condition = optimal
results.problem.lower_bound = <local incumbent>
results.problem.upper_bound = <same local incumbent>

For benchmark and downstream tooling, that is indistinguishable from a globally certified solve unless the caller already knows the model is nonconvex and knows this GDPopt LOA caveat.

Minimal result-finalization reproducer

This reproducer does not require external solvers. It isolates the relevant result semantics: when a LOA run has a local primal incumbent and a non-rigorous OA/discrete bound that has crossed it, the generic GDPopt convergence logic force-updates the dual bound to the primal bound and returns optimal with equal bounds.

import logging

import pyomo.environ as pyo
from pyomo.common.timing import default_timer
from pyomo.contrib.gdpopt.loa import GDP_LOA_Solver
from pyomo.opt import SolverResults

solver = GDP_LOA_Solver()
solver.pyomo_results = SolverResults()
solver.pyomo_results.problem.sense = pyo.maximize

# This mimics a nonconvex LOA state:
# - LB is a feasible incumbent from a local NLP subproblem.
# - UB is the OA/discrete bound. For a nonconvex problem this bound is not
#   necessarily globally valid, and it has crossed the incumbent.
solver.LB = 1011.6577899409375
solver.UB = 1000.0
solver.iteration = 1
solver.timing.main_timer_start_time = default_timer()
solver.timing.total = 0.0

config = solver.CONFIG()
config.bound_tolerance = 1e-6
config.logger = logging.getLogger("gdpopt-loa-mwe")
config.logger.handlers[:] = [logging.StreamHandler()]
config.logger.setLevel(logging.INFO)

print("before", solver.LB, solver.UB, solver.pyomo_results.solver.termination_condition)
print("converged", solver.bounds_converged(config))
print("after", solver.LB, solver.UB, solver.pyomo_results.solver.termination_condition)

results = solver._get_final_pyomo_results_object()
print(
    "results",
    results.problem.lower_bound,
    results.problem.upper_bound,
    results.solver.termination_condition,
)

Observed output with Pyomo 6.10.0:

        1                      1011.65779    1011.65779      0.00%      0.00
GDPopt exiting--bounds have converged or crossed.
before 1011.6577899409375 1000.0 unknown
converged True
after 1011.6577899409375 1011.6577899409375 optimal
results 1011.6577899409375 1011.6577899409375 optimal

The problematic behavior is not that the internal crossed-bound logic exists for algorithms with rigorous bounds. The problematic behavior is that LOA uses the same finalization path even though its dual bound can be non-rigorous on nonconvex models.

Downstream evidence from GDPLib

This surfaced while benchmarking GDPLib's HDA model:

GDPLib HDA issue: Refactor hda to fix benchmark issues SECQUOIA/gdplib#67
GDPLib PR: Fix hda hull and GLOA benchmark paths SECQUOIA/gdplib#130
GDPLib central benchmark tracker: Central tracker: model benchmark failures across GDP strategies SECQUOIA/gdplib#60

For the HDA instance, the local LOA benchmark row reported:

strategy: gdpopt.loa
solver profile: gams-local
termination: optimal
lower bound: 1011.6577899409375
upper bound: 1011.6577899409375
iterations: 1

However, the HDA model is nonconvex, and other GDPopt/global-capable routes found a better feasible solution:

gdpopt.gloa + gams-local: optimal, objective 1105.3441871686007
gdpopt.ric + gams-local: optimal, objective 1105.3441871686007
gdpopt.ric + gams-gurobi: optimal, objective 1105.3441871686007
gdpopt.ric + gams-baron: optimal, objective 1105.339918385673

For a maximization problem, a reported LOA upper bound of 1011.6577899409375 is therefore not a valid global upper bound once a feasible point around 1105.34 is known. The LB = UB result gives the appearance of a globally certified incumbent even though it is a local/non-rigorous LOA result.

Expected behavior

For LOA on models where the OA/discrete bound is not known to be rigorous, GDPopt should avoid returning globally certified-looking result metadata.

Possible approaches:

Return a non-global termination condition such as feasible or locallyOptimal when LOA converges only by non-rigorous/crossed bounds on a nonconvex problem.
Preserve the incumbent as the primal bound but avoid force-setting the dual bound equal to the incumbent when the dual bound is not rigorous.
Add explicit result metadata indicating that the reported bound is not rigorous.
Add an option such as assume_convex=True/False or certify_bounds=True/False, with conservative default result semantics for LOA unless convexity/global validity is asserted.

The important downstream requirement is that JSON/benchmark consumers should not have to infer from solver.name == "GDPopt ... - LOA" that optimal and LB = UB may not mean globally optimal.

Environment

Observed locally with:

Python 3.12.13
Pyomo 6.10.0
OS/platform: Linux WSL2, glibc 2.39

I added a full model MWE here, in addition to the solver-free result-finalization reproducer in the issue body.

This example uses open solvers (glpk for the MILP master and ipopt for NLP subproblems). It is intentionally small: the reported LOA upper bound is invalidated by an explicit feasible point in the other disjunct.

import math

import pyomo.environ as pyo
from pyomo.gdp import Disjunct, Disjunction


def build_model():
    m = pyo.ConcreteModel()
    m.x = pyo.Var(bounds=(0, 4), initialize=0.2)
    m.y = pyo.Var(bounds=(-2, 2), initialize=0)

    # Nonconvex feasible region: y <= sin(3*x) + 0.2*x.
    m.nonconvex = pyo.Constraint(expr=m.y <= pyo.sin(3 * m.x) + 0.2 * m.x)

    # A small GDP structure. The better feasible point is in the right branch,
    # but LOA terminates after the left-branch local solution.
    m.left = Disjunct()
    m.right = Disjunct()
    m.left.region = pyo.Constraint(expr=m.x <= 2)
    m.right.region = pyo.Constraint(expr=m.x >= 2)
    m.choose_region = Disjunction(expr=[m.left, m.right], xor=True)

    m.obj = pyo.Objective(expr=m.y, sense=pyo.maximize)
    return m


model = build_model()
results = pyo.SolverFactory("gdpopt.loa").solve(
    model,
    mip_solver="glpk",
    nlp_solver="ipopt",
    init_algorithm="set_covering",
    bound_tolerance=1e-6,
    tee=False,
)

print("LOA termination:", results.solver.termination_condition)
print("LOA lower bound:", results.problem.lower_bound)
print("LOA upper bound:", results.problem.upper_bound)
print("LOA incumbent x:", pyo.value(model.x))
print("LOA incumbent y:", pyo.value(model.y))
print("left indicator:", model.left.indicator_var.value)
print("right indicator:", model.right.indicator_var.value)

# An explicit feasible point in the right disjunct. This is enough to show that
# the LOA-reported upper bound is not a valid global upper bound.
x_feas = 2.6404
y_feas = math.sin(3 * x_feas) + 0.2 * x_feas
print("explicit feasible x:", x_feas)
print("explicit feasible y:", y_feas)
print("feasible y exceeds reported upper bound:", y_feas > results.problem.upper_bound)

Observed output with Pyomo 6.10.0:

LOA termination: optimal
LOA lower bound: 1.1069428089835942
LOA upper bound: 1.1069428089835942
LOA incumbent x: 0.5458374919734859
LOA incumbent y: 1.1069428089835942
left indicator: True
right indicator: False
explicit feasible x: 2.6404
explicit feasible y: 1.5258216961360678
feasible y exceeds reported upper bound: True

The explicit point x = 2.6404, y = sin(3*x) + 0.2*x = 1.5258216961360678 satisfies the right disjunct (x >= 2) and the nonlinear constraint. For this maximization model, that means the reported LOA upper bound 1.1069428089835942 is not a valid global upper bound. The issue is therefore not only that LOA found a local solution, but that the returned SolverResults fields present it as optimal with LB = UB.

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GDPopt LOA reports non-rigorous nonconvex bounds as optimal LB=UB #3947

Summary

Minimal result-finalization reproducer

Downstream evidence from GDPLib

Expected behavior

Environment

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GDPopt LOA reports non-rigorous nonconvex bounds as optimal LB=UB #3947

Description

Summary

Minimal result-finalization reproducer

Downstream evidence from GDPLib

Expected behavior

Environment

Activity

bernalde commented on May 11, 2026

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