A Decomposition Framework for Nonlinear Nonconvex Two-Stage Optimization
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866910034384912384 |
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| author | Lou, Yuchen Luo, Xinyi Wächter, Andreas Wei, Ermin |
| author_facet | Lou, Yuchen Luo, Xinyi Wächter, Andreas Wei, Ermin |
| contents | We propose a new decomposition framework for continuous nonlinear constrained two-stage optimization, where both first- and second-stage problems can be nonconvex. A smoothing technique based on an interior-point formulation renders the optimal solution of the second-stage problem differentiable with respect to the first-stage parameters. As a consequence, efficient off-the-shelf optimization packages can be utilized. We show that the solution of the nonconvex second-stage problem behaves locally like a differentiable function so that existing proofs can be applied to prove the convergence of the iterates to first-order optimal points for the first-stage. We also prove fast local convergence of the algorithm as the barrier parameter is driven to zero. Numerical experiments for large-scale instances demonstrate the computational advantages of the decomposition framework. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_11700 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Decomposition Framework for Nonlinear Nonconvex Two-Stage Optimization Lou, Yuchen Luo, Xinyi Wächter, Andreas Wei, Ermin Optimization and Control We propose a new decomposition framework for continuous nonlinear constrained two-stage optimization, where both first- and second-stage problems can be nonconvex. A smoothing technique based on an interior-point formulation renders the optimal solution of the second-stage problem differentiable with respect to the first-stage parameters. As a consequence, efficient off-the-shelf optimization packages can be utilized. We show that the solution of the nonconvex second-stage problem behaves locally like a differentiable function so that existing proofs can be applied to prove the convergence of the iterates to first-order optimal points for the first-stage. We also prove fast local convergence of the algorithm as the barrier parameter is driven to zero. Numerical experiments for large-scale instances demonstrate the computational advantages of the decomposition framework. |
| title | A Decomposition Framework for Nonlinear Nonconvex Two-Stage Optimization |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2501.11700 |