Sensitivity Analysis

POUNCE includes a parametric sensitivity capability compatible with upstream Ipopt’s contrib/sIPOPT/ (Pirnay, López-Negrete & Biegler 2012, DOI 10.1007/s12532-012-0043-2). It computes the first-order change in the optimal primal solution with respect to a problem parameter, reusing the KKT factorization from the converged solve. Three entry points cover the common workflows.

AMPL CLI

The main pounce driver auto-detects the sIPOPT suffixes (sens_state_1, sens_state_value_1, sens_init_constr) in an input .nl, runs a post-optimal sensitivity step after the solve, and writes the perturbed primal back as a sens_sol_state_1 suffix — no separate binary or flag needed:

pounce problem.nl                   # writes problem.sol
pounce problem.nl out.sol --json-output result.json --json-detail full

pounce_sens is retained as a thin backward-compatibility alias: pounce_sens in.nl out.sol is identical to pounce in.nl out.sol, so existing AMPL / solver scripts keep working unchanged.

Related flags:

• --sens-boundcheck / --sens-bound-eps EPS — clamp the perturbed primal x* + Δx onto the declared [x_l, x_u] box.
• --compute-red-hessian / --rh-eigendecomp — compute the reduced Hessian (and its eigendecomposition) over the variables tagged by the red_hessian integer var-suffix.

Rust library

SensSolve is a builder that wraps the on_converged callback plumbing into a single call:

#![allow(unused)]
fn main() {
use pounce_sensitivity::SensSolve;

let result = SensSolve::new(vec![2, 3])
    .with_deltas(vec![0.05, 0.0])
    .with_reduced_hessian()
    .run(&mut app, tnlp);
// result.dx, result.reduced_hessian, result.status
}

with_reduced_hessian_eigen() adds the eigendecomposition; with_boundcheck(eps) enables the bound projection.

Python

solve_with_sens exposes the same capability from the cyipopt-compatible Python wrapper:

# pin_constraint_indices is required; pass deltas=..., compute_reduced_hessian=True,
# or both. Returns (x, info) — sensitivity outputs live in the info dict.
x, info = prob.solve_with_sens(x0, pin_constraint_indices=[2, 3],
                               deltas=[0.05, 0.0], sens_boundcheck=True)
# info["dx"], info["reduced_hessian"], info["reduced_hessian_eigenvalues"], ...

compute_reduced_hessian=True returns the reduced Hessian in info["reduced_hessian"]; rh_eigendecomp=True adds its eigendecomposition; sens_bound_eps=… tunes the bound projection. See python/notebooks/04_sensitivity.ipynb for a walkthrough.

Verification

All three entry points are verified against upstream sIPOPT 3.14.19’s parametric_cpp golden output to within roughly 6e-9 per component. The bound projection is a single-pass clamp; upstream’s iterative Schur refinement (re-factorize on each violation) is intentionally not ported.