Globally Optimal Estimation of Nested Logit Models

Hoang Giang Pham and Tien Mai

Papers from arXiv.org

Abstract: Nested logit is widely used in operational demand models, yet jointly estimating its utility coefficients and nest dissimilarity parameters requires nonconvex optimization. Standard estimation routines offer no certificate of global optimality, leaving a gap between globally optimizing decisions under nested-logit demand and reliably estimating that demand model. We develop, to our knowledge, the first globally convergent optimization framework with an explicit global-accuracy guarantee for joint nested-logit estimation. Our central complexity result confines all exponential dependence to the number of free nest dissimilarity parameters: computation is polynomial in the numbers of observations, alternatives, and utility coefficients. Consequently, under the stated compact-domain and relaxation-error conditions, fixing the number of nests yields an additive polynomial-time approximation scheme (PTAS). The framework exploits an exact exponential-cone formulation for fixed dissimilarities and a spatial branch-and-bound algorithm that searches only over the free dissimilarities. Valid likelihood bounds provide an anytime certificate and finite termination at any prescribed additive average-log-likelihood tolerance. Across eight benchmark datasets and 240 estimation instances, the method certifies every reported solution and exposes inferior local estimates despite normal solver termination. These results establish a computational foundation for globally certified nested-logit estimation.

Date: 2026-10
New Economics Papers: this item is included in nep-dcm and nep-ecm
References: Add references at CitEc
Citations:

Downloads: (external link)
https://arxiv.org/pdf/2610.25038 Latest version (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:arx:papers:2610.25038

Access Statistics for this paper

More papers in Papers from arXiv.org
Bibliographic data for series maintained by arXiv administrators ().