An Alternating Direction Method of Multipliers for Topology Optimization
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866916967225491456 |
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| author | Choudhary, Harsh Leyffer, Sven Yang, Dominic |
| author_facet | Choudhary, Harsh Leyffer, Sven Yang, Dominic |
| contents | We consider a class of integer-constrained optimization problems governed by partial differential equation (PDE) constraints and regularized via total variation (TV) in the context of topology optimization. The presence of discrete design variables, nonsmooth regularization, and non-convex objective renders the problem computationally challenging. To address this, we adopt the alternating direction method of multipliers (ADMM) framework, which enables a decomposition of the original problem into simpler subproblems that can be solved efficiently. The augmented Lagrangian formulation ensures consistency across variable updates while facilitating convergence under appropriate conditions. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2509_19888 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | An Alternating Direction Method of Multipliers for Topology Optimization Choudhary, Harsh Leyffer, Sven Yang, Dominic Optimization and Control Numerical Analysis We consider a class of integer-constrained optimization problems governed by partial differential equation (PDE) constraints and regularized via total variation (TV) in the context of topology optimization. The presence of discrete design variables, nonsmooth regularization, and non-convex objective renders the problem computationally challenging. To address this, we adopt the alternating direction method of multipliers (ADMM) framework, which enables a decomposition of the original problem into simpler subproblems that can be solved efficiently. The augmented Lagrangian formulation ensures consistency across variable updates while facilitating convergence under appropriate conditions. |
| title | An Alternating Direction Method of Multipliers for Topology Optimization |
| topic | Optimization and Control Numerical Analysis |
| url | https://arxiv.org/abs/2509.19888 |