Scalable Co-Design via Linear Design Problems: Compositional Theory and Algorithms
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| Format: | Preprint |
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2026
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| _version_ | 1866911556245127168 |
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| author | Cai, Yubo Huang, Yujun Alharbi, Meshal Zardini, Gioele |
| author_facet | Cai, Yubo Huang, Yujun Alharbi, Meshal Zardini, Gioele |
| contents | Designing complex engineered systems requires managing tightly coupled trade-offs between subsystem capabilities and resource requirements. Monotone co-design provides a compositional language for such problems, but its generality does not by itself reveal which problem classes admit exact and scalable computation. This paper isolates such a class by introducing Linear Design Problems (LDPs): design problems whose feasible functionality--resource relations are polyhedra over Euclidean posets. We show that queries on LDPs reduce exactly to Multi-Objective Linear Programs (MOLPs), thereby connecting monotone co-design semantics with polyhedral multiobjective optimization. We further prove that LDPs are closed under the fundamental co-design interconnections, implying that any interconnection of linear components induces a system-level LDP. To compute the resulting feasible sets, we develop two complementary constructions: a monolithic lifted formulation that preserves block-angular sparsity, and a compositional formulation that incrementally eliminates internal variables through polyhedral projection. Beyond the exact linear setting, we show that convex co-design resource queries admit arbitrarily accurate polyhedral outer approximations, with recession-cone error identically zero for standard nonnegative resource cones. Numerical studies on synthetic series-chain benchmarks, a gripper, and a rover co-design validate the theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_29083 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Scalable Co-Design via Linear Design Problems: Compositional Theory and Algorithms Cai, Yubo Huang, Yujun Alharbi, Meshal Zardini, Gioele Optimization and Control Systems and Control Designing complex engineered systems requires managing tightly coupled trade-offs between subsystem capabilities and resource requirements. Monotone co-design provides a compositional language for such problems, but its generality does not by itself reveal which problem classes admit exact and scalable computation. This paper isolates such a class by introducing Linear Design Problems (LDPs): design problems whose feasible functionality--resource relations are polyhedra over Euclidean posets. We show that queries on LDPs reduce exactly to Multi-Objective Linear Programs (MOLPs), thereby connecting monotone co-design semantics with polyhedral multiobjective optimization. We further prove that LDPs are closed under the fundamental co-design interconnections, implying that any interconnection of linear components induces a system-level LDP. To compute the resulting feasible sets, we develop two complementary constructions: a monolithic lifted formulation that preserves block-angular sparsity, and a compositional formulation that incrementally eliminates internal variables through polyhedral projection. Beyond the exact linear setting, we show that convex co-design resource queries admit arbitrarily accurate polyhedral outer approximations, with recession-cone error identically zero for standard nonnegative resource cones. Numerical studies on synthetic series-chain benchmarks, a gripper, and a rover co-design validate the theory. |
| title | Scalable Co-Design via Linear Design Problems: Compositional Theory and Algorithms |
| topic | Optimization and Control Systems and Control |
| url | https://arxiv.org/abs/2603.29083 |