Pith Number

pith:MPPOH5RY

pith:2026:MPPOH5RYGKXSC3RSLDDGX4AVKD

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Inexact Adjoint Gradients and Directional Tolerances for Full-Potential Airfoil Optimization

Humberto Gimenes Macedo, Lu\'is Felipe Bueno

Inexact adjoint gradients satisfy exact descent inequalities under directional tolerances derived from residual bounds.

arxiv:2605.17599 v1 · 2026-05-17 · math.OC

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Claims

C1strongest claim

On compact sets of decision variables, a uniform version of this bound is obtained, leading to a directional tolerance condition under which the inexact gradient satisfies an exact descent inequality. The resulting inexact general directions method inherits convergence properties under uniformly bounded, diminishing, and Armijo-type step-size rules.

C2weakest assumption

The gradient-error bound and subsequent directional tolerance hold when the state and adjoint residuals are affine in the state variable; this assumption is invoked to obtain the linear combination bound on gradient error (see theoretical part of abstract).

C3one line summary

Connects inexact discrete adjoint gradient bounds to directional tolerances that guarantee descent and convergence in full-potential airfoil pressure-matching optimization.

References

7 extracted · 7 resolved · 0 Pith anchors

[1] D. P. Bertsekas,Nonlinear Programming, Athena Scientific, 3rd ed., 2016 2016

[2] T. G. Kolda and B. W. Bader, Tensor decompositions and applications,SIAM Review, 51 (2009), pp. 455–500 2009

[3] G. K. W. Kenway, C. A. Mader, P. He, and J. R. R. A. Martins, Effective adjoint approaches for computational fluid dynamics,Progress in Aerospace Sciences, 110 (2019), 100542 2019

[4] P. D. Khanh, B. S. Mordukhovich, and D. B. Tran, Inexact reduced gradient methods with adaptive error control, 2024 2024

[5] T. L. Holst, Implicit algorithm for the conservative transonic full-potential equation using an arbitrary mesh,AIAA Journal, 17 (1979), pp. 1038–1045 1979

Formal links

1 machine-checked theorem link

Receipt and verification

First computed	2026-05-20T00:04:47.909695Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

63dee3f63832af216e3258c66bf01550e01d372abe5dc52718d5b05dfa7977ec

Aliases

arxiv: 2605.17599 · arxiv_version: 2605.17599v1 · doi: 10.48550/arxiv.2605.17599 · pith_short_12: MPPOH5RYGKXS · pith_short_16: MPPOH5RYGKXSC3RS · pith_short_8: MPPOH5RY

Agent API

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/MPPOH5RYGKXSC3RSLDDGX4AVKD \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 63dee3f63832af216e3258c66bf01550e01d372abe5dc52718d5b05dfa7977ec

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "13a98cc0ba11c6c31a1d51a1cc773bd5f64deea7c97977622943989659717dbe",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2026-05-17T18:52:16Z",
    "title_canon_sha256": "b6202fd76a8f4907ab19e89d0a1d8e3e7e407d2e6fae22fc5358259aa0950154"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.17599",
    "kind": "arxiv",
    "version": 1
  }
}