Pith Number

pith:FOWWRGIZ

pith:2026:FOWWRGIZC4N5GQYTN3REZ2OQI4

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Multiconic Optimization for Symmetric Cones and Hyperbolic Coupling

Marianna E.-Nagy, Petra Ren\'ata Rig\'o, Yurii Nesterov

A new interior-point algorithm using hyperbolic coupling solves multiconic optimization over symmetric cones with complexity matching linear programming.

arxiv:2605.12658 v1 · 2026-05-12 · math.OC

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Claims

C1strongest claim

We justify all main steps in the complexity analysis of the algorithm and prove that the overall complexity of solving this type of large-scale nonlinear problems by our algorithm is comparable with the best known complexity for solving linear programming problems of the same dimension.

C2weakest assumption

The hyperbolic coupling provides a controllable framework for interdependent primal-dual pairs that enables the claimed complexity analysis without hidden gaps or additional assumptions on cone dimensions.

C3one line summary

A new interior-point method for multiconic problems achieves LP-level complexity through hyperbolic coupling of primal-dual variables in a parabolic target space.

References

20 extracted · 20 resolved · 0 Pith anchors

[1] S. Asadi, N. Mahdavi-Amiri, Z. Darvay, and P. R. Rig´ o. Full Nesterov-Todd step feasible interior-point algorithm for symmetric cone horizontal linear complementarity problem based on a positive-asym 2020

[2] S. Asadi, H. Mansouri, Z. Darvay, and M. Zangiabadi. On theP ∗(κ) horizontal linear com- plementarity problems over Cartesian product of symmetric cones.Optim. Methods Softw., 31(2):233–257, 2016 2016

[3] S. Asadi, H. Mansouri, G. Lesaja, and M. Zangiabadi. A long-step interior-point algorithm for symmetric cone CartesianP ∗(κ)-HLCP.Optimization, 67(11):2031–2060, 2018 2031

[4] M. E.-Nagy, T. Ill´ es, Yu. Nesterov, and P.R. Rig´ o. Parabolic target space interior-point algorithms for weighted monotone linear complementarity problem.Math. Program., 2025. https://doi.org/10.10 2025 · doi:10.1007/s10107-025-02260-x

[5] M. E.-Nagy, T. Ill´ es, Yu. Nesterov, and P.R. Rig´ o. New interior-point algorithm for linear op- timization based on a universal tangent direction.SIAM J. Optim., 36(1):185–203, 2026 2026

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Receipt and verification

First computed	2026-05-18T03:09:50.590052Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2bad689919171bd343136ee24ce9d0470fc673f8355c61f01895f7c11902ea47

Aliases

arxiv: 2605.12658 · arxiv_version: 2605.12658v1 · doi: 10.48550/arxiv.2605.12658 · pith_short_12: FOWWRGIZC4N5 · pith_short_16: FOWWRGIZC4N5GQYT · pith_short_8: FOWWRGIZ

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/FOWWRGIZC4N5GQYTN3REZ2OQI4 \
  | 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: 2bad689919171bd343136ee24ce9d0470fc673f8355c61f01895f7c11902ea47

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "47a978c785c92c39d171a8a9d322b0c978525bf8e8bb0a56a24945ffd48608b5",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2026-05-12T19:05:14Z",
    "title_canon_sha256": "0ea198727da8698694d785d7661462098fc7f5049e3a7616a7966f378a75cdc1"
  },
  "schema_version": "1.0",
  "source": {
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    "kind": "arxiv",
    "version": 1
  }
}