Hidden convexity property of a speed planning problem
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912674503196672 |
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| author | Ardizzoni, Stefano Consolini, Luca Laurini, Mattia Locatelli, Marco |
| author_facet | Ardizzoni, Stefano Consolini, Luca Laurini, Mattia Locatelli, Marco |
| contents | In this paper we address the speed planning problem for a vehicle along a predefined path. A weighted average of two (conflicting) terms, energy consumption and travel time, is minimized. After deriving a non-convex mathematical model of the problem, we introduce a convex relaxation of the model and show that, after the application of a suitable feasibility-based bound tightening procedure, the convex relaxation shares the same optimal value and solution of the non-convex problem. We also establish that the feasible region of the non-convex problem is a lattice and, through that, a necessary and sufficient condition for the non-emptiness of the feasible region. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_09424 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Hidden convexity property of a speed planning problem Ardizzoni, Stefano Consolini, Luca Laurini, Mattia Locatelli, Marco Optimization and Control In this paper we address the speed planning problem for a vehicle along a predefined path. A weighted average of two (conflicting) terms, energy consumption and travel time, is minimized. After deriving a non-convex mathematical model of the problem, we introduce a convex relaxation of the model and show that, after the application of a suitable feasibility-based bound tightening procedure, the convex relaxation shares the same optimal value and solution of the non-convex problem. We also establish that the feasible region of the non-convex problem is a lattice and, through that, a necessary and sufficient condition for the non-emptiness of the feasible region. |
| title | Hidden convexity property of a speed planning problem |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2503.09424 |