Pith Number

pith:CDOGN3FA

pith:2025:CDOGN3FAU6KYDXI7H44LUUX3WS

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A Hybrid Learning-to-Optimize Framework for Mixed-Integer Quadratic Programming

Mu Xie, Rahul Mangharam, Viet-Anh Le

A neural network predicts integer variables in parametric mixed-integer quadratic programs while a differentiable QP layer solves for the continuous part using a hybrid loss.

arxiv:2511.19383 v2 · 2025-11-24 · eess.SY · cs.SY

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Claims

C1strongest claim

a neural network (NN) is used to learn the mapping from problem parameters to optimal integer solutions, while a differentiable QP layer is integrated to compute the corresponding continuous variables given the predicted integers and problem parameters. Moreover, a hybrid loss function is proposed, which combines a supervised loss with respect to the global optimal solution, and a self-supervised loss derived from the problem's objective and constraints.

C2weakest assumption

That a neural network trained on a finite set of problem instances will produce integer predictions whose corresponding QP solutions remain near-optimal and feasible for unseen parameter values encountered at runtime.

C3one line summary

A hybrid L2O framework predicts optimal integer solutions for MIQP via neural network, recovers continuous variables with a differentiable QP layer, and trains with supervised optimality loss plus self-supervised feasibility loss.

References

15 extracted · 15 resolved · 1 Pith anchors

[1] Differentiable convex optimization layers 2019

[2] Optnet: Differentiable optimization as a layer in neural networks 2017

[3] Formal methods for control synthesis: An optimization perspective 2019

[4] Estimating or Propagating Gradients Through Stochastic Neurons for Conditional Computation 2013 · arXiv:1308.3432

[5] Constrained optimization and Lagrange multiplier methods 2014

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-18T02:44:32.357173Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

10dc66eca0a79581dd1f3f38ba52fbb49e88bd9e38b68e1a2fa54c21d157b926

Aliases

arxiv: 2511.19383 · arxiv_version: 2511.19383v2 · doi: 10.48550/arxiv.2511.19383 · pith_short_12: CDOGN3FAU6KY · pith_short_16: CDOGN3FAU6KYDXI7 · pith_short_8: CDOGN3FA

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/CDOGN3FAU6KYDXI7H44LUUX3WS \
  | 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: 10dc66eca0a79581dd1f3f38ba52fbb49e88bd9e38b68e1a2fa54c21d157b926

Canonical record JSON

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    "abstract_canon_sha256": "8c3f644383d1262fce22e7a864ff7d9853003d206eff4ef944e5bc2d6cae0a30",
    "cross_cats_sorted": [
      "cs.SY"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "eess.SY",
    "submitted_at": "2025-11-24T18:22:00Z",
    "title_canon_sha256": "ca5c12e5ff3b1d9773cc861a2364a28bcb2b628b7bf860e5b558a6d9499aba05"
  },
  "schema_version": "1.0",
  "source": {
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    "kind": "arxiv",
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  }
}