Abstract:The Hamiltonian Path Problem is formulated as a continuous minimization problem on conductances assigned to an Ohmic network associated with the given graph. The objective function is a sum of two penalty terms that collectively enforce a set of conditions sufficient for a subgraph of the original graph to be a Hamiltonian path. The objective function is nonconvex. The main result (Theorem 1) shows that, provided the graph has a Hamiltonian path from $h^{start}$ to $h^{end}$, a conductance configuration is a global minimizer of the objective if and only if it corresponds to a Hamiltonian path.
| Comments: | 10 pages |
| Subjects: | Optimization and Control (math.OC) |
| Cite as: | arXiv:2605.24289 [math.OC] |
| (or arXiv:2605.24289v1 [math.OC] for this version) | |
| https://doi.org/10.48550/arXiv.2605.24289 arXiv-issued DOI via DataCite (pending registration) |
From: Alexander Sadovsky [view email]
[v1]
Fri, 22 May 2026 23:42:10 UTC (10 KB)
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