These explicit workflows use ordinary Continuous linear models and numerical HiGHS semantics. They do not automatically relax a MIP or replace unsupported indicators/globals. Historical artifacts own their source model and original slot mapping. Available zero values, unavailable data and unrequested data have different states; read those states before optional payloads.

Operation	Delivered data	Boundary
Gecode::Optimize::solve_lp_observed	Original row activity/slack, checked duals/reduced costs and basis statuses	Accepted duals require timely optimal primal/dual data and independent KKT checks. Basis data is not a proof.
Gecode::Optimize::make_lp_basis and Gecode::Optimize::solve_lp_with_basis	Immutable original basis input and explicit accepted/repaired/rejected submission	Exact owner/revision/content checks; no simultaneous primal start, silent cold fallback or faster-solve guarantee.
Gecode::Optimize::analyze_lp_evidence	Independently checked numerical primal rays or Farkas multipliers using explicit private auxiliary solves	Original and auxiliary coordinates/statuses remain distinct; no exact infeasibility certificate claim.
Gecode::Optimize::analyze_lp_sensitivity	One-parameter objective-coefficient or common equality-RHS interval for a selected optimal basis	Additional private factorization/system solves, zero optimization runs; numerical intervals only.

Selected-basis sensitivity

LpSensitivityOptions requests unique LpObjectiveParameter or LpEqualityRhsParameter entries from an owning LpObservedResult. The analyzer checks original feasibility, dual/KKT evidence, complete basis statuses and reconstructed reference point before interval publication. It neither repairs nor chooses another basis. A degenerate optimum can have different intervals for different selected bases/statuses.

namespace O = Gecode::Optimize;
O::Model model;
const auto x = model.add_continuous();
const auto y = model.add_continuous();
const auto balance = model.add_row({{x, 1}, {y, 1}}, 3, 3);
model.minimize({{x, 2}, {y, 1}}, 7);
const auto observed = O::solve_lp_observed(model);
O::LpSensitivityOptions options;
options.parameters = {O::LpObjectiveParameter{x},
                      O::LpEqualityRhsParameter{balance}};
const auto analysis = O::analyze_lp_sensitivity(observed, options);
if (analysis.sensitivity) {
  const auto* entry = analysis.sensitivity->objective(x);
  if (entry && entry->group.state == O::LpSensitivityState::Available) {
    // Read entry->interval: tagged endpoints, slope and checks.
  }
}

Each interval varies one original parameter alone with the selected basis and nonbasic statuses fixed. Equality RHS varies both equal sides together. Endpoints are absolute parameter values; infinity is tagged, not a finite double. A singleton is an available interval. The optional objective_slope describes slope*(parameter-anchor), without adding the original offset again. Variable-bound, inequality-side, matrix-entry and simultaneous perturbation ranges are not supported. There is no CPLEX/Gurobi ranging equivalence claim.

Complete means every requested interval passed; Partial allows per-request rejection. Whole-call stop, resource, allocation or cleanup failure clears every interval's availability, including earlier results. Source history and completed diagnostics can remain. Lookups perform no solver work and survive model/session destruction. Size/work/factor-solve caps and one cooperative deadline cover admission through backend cleanup.