Pith Number

pith:V7MX236T

pith:2026:V7MX236TZ2S4HLFD5O2F77E7WQ

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Generalized Dual Decomposition

Pengyu Zhang, Ruiwei Jiang

Generalized dual decomposition replaces the linear regularizer with a nonlinear one to restore strong duality while keeping parallel subproblem solves in two-stage mixed-integer stochastic programs.

arxiv:2605.14273 v1 · 2026-05-14 · math.OC

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Claims

C1strongest claim

we propose a generalized dual decomposition (GDD) that extends the linear regularizer used in dual decomposition to a general nonlinear one, which still admits parallelization while exhibiting strong duality... we establish the convergence of a GDD algorithm to achieve global optimum.

C2weakest assumption

That nonlinear regularizers can be encoded through parameterization and cutting planes in a way that preserves both parallelizability and strong duality without introducing post-hoc data-dependent choices that invalidate the global-optimality guarantee.

C3one line summary

Generalized Dual Decomposition replaces linear regularizers with nonlinear ones in dual decomposition to achieve strong duality and global optimality for mixed-integer two-stage stochastic programs while retaining parallelization.

References

17 extracted · 17 resolved · 0 Pith anchors

[1] Defineg ′ i(x) := PN i′=1 fi′(x) N −f i(x),∀i∈[N]

[2] inf x∈X lim infh(x) = inf x∈X limϵ→0 inf x′∈X∩B(x,ϵ) h(x′) ≥inf x∈X limϵ→0 (inf x′∈X h(x′)) = inf x∈X h(x)

[3] Thus inf x∈X h(x) = infx∈X lim infh(x)

[4] Thus,∥c(x i (r))− ˜xi∗∥ ≤ ∥c(xi (r))−x i (r)∥+∥x i (r) − ˜xi∗∥ ≤ ∥xi (R′) −x i (r)∥+∥x i (r) − ˜xi∗∥ ≤ 2ϵ 3 + ϵ 3 =ϵ. It follows that lim inf r→∞ gi(X t(r),x i (r)) = lim inf r→∞ g∗ i (c(xi (r))) (4)

[5] Zhang and Jiang:Generalized Dual Decomposition 39

Formal links

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Receipt and verification

First computed	2026-05-17T23:39:10.372901Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

afd97d6fd3cea5c3aca3ebb45ffc9fb41ea626c36a7fe48e881312a4daf31d8c

Aliases

arxiv: 2605.14273 · arxiv_version: 2605.14273v1 · doi: 10.48550/arxiv.2605.14273 · pith_short_12: V7MX236TZ2S4 · pith_short_16: V7MX236TZ2S4HLFD · pith_short_8: V7MX236T

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curl -sH 'Accept: application/ld+json' https://pith.science/pith/V7MX236TZ2S4HLFD5O2F77E7WQ \
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Canonical record JSON

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  "metadata": {
    "abstract_canon_sha256": "b55f687bd2df8a52d66940a969abf4edec87815454fc7275e19c9ec8a7a32f4c",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2026-05-14T02:16:35Z",
    "title_canon_sha256": "fb09c54635444a322876ee09066f21a0a83b1c48b95a93518ac8ed682afc5e89"
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