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| Format: | Preprint |
| Veröffentlicht: |
2026
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| Online-Zugang: | https://arxiv.org/abs/2605.14273 |
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| _version_ | 1866909041609932800 |
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| author | Zhang, Pengyu Jiang, Ruiwei |
| author_facet | Zhang, Pengyu Jiang, Ruiwei |
| contents | We study two-stage stochastic optimization models with mixed-integer decision variables appearing in both stages. For these models, dual decomposition enables parallel computing implementation and can quickly provide a lower bound for the optimal value. However, the lower bound thus obtained is not exact in general due to the lack of strong duality. In this paper, 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. By encoding the nonlinear regularizers through parameterization and cutting planes, we establish the convergence of a GDD algorithm to achieve global optimum. In addition, we discuss strategies for solving the GDD scenario subproblems more efficiently, including pruning and valid inequalities. Furthermore, we extend GDD to a more general, constrained form that subsumes, as special cases, robust optimization, chance-constrained programs, and bilevel optimization with multiple followers. Finally, numerical experiments demonstrate the strong duality of GDD, its computational efficacy versus primal (Benders-type) decomposition algorithms, and the speedup through parallel computing. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_14273 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Generalized Dual Decomposition Zhang, Pengyu Jiang, Ruiwei Optimization and Control We study two-stage stochastic optimization models with mixed-integer decision variables appearing in both stages. For these models, dual decomposition enables parallel computing implementation and can quickly provide a lower bound for the optimal value. However, the lower bound thus obtained is not exact in general due to the lack of strong duality. In this paper, 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. By encoding the nonlinear regularizers through parameterization and cutting planes, we establish the convergence of a GDD algorithm to achieve global optimum. In addition, we discuss strategies for solving the GDD scenario subproblems more efficiently, including pruning and valid inequalities. Furthermore, we extend GDD to a more general, constrained form that subsumes, as special cases, robust optimization, chance-constrained programs, and bilevel optimization with multiple followers. Finally, numerical experiments demonstrate the strong duality of GDD, its computational efficacy versus primal (Benders-type) decomposition algorithms, and the speedup through parallel computing. |
| title | Generalized Dual Decomposition |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2605.14273 |