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A bounded degree SDSOS hierarchy for solving SPLD polynomial programs
Abstract
A polynomial optimization problem is said to have an SPLD structure if the polynomials defining its objective and constraints admit decompositions into separable and nonseparable parts, with the maximum degree of the separable parts exceeding that of the nonseparable parts. In this paper, we propose a bounded degree SDSOS hierarchy for globally solving a class of such problems. We establish the asymptotic convergence of this hierarchy over compact feasible sets and provide a sufficient condition for its finite convergence. Numerical experiments compare the proposed hierarchy with the BSDSOS hierarchy (Chuong et al. in J. Global Optim., 75(4):885-919, 2019).
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BibTeX
@misc{yang2026bounded,
title = {{A bounded degree SDSOS hierarchy for solving SPLD polynomial programs}},
author = {Chengmiao Yang and Liguo Jiao and Jae Hyoung Lee},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.41483},
eprint = {2610.41483},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.41483},
}
RIS
TY - UNPB
TI - A bounded degree SDSOS hierarchy for solving SPLD polynomial programs
AU - Chengmiao Yang
AU - Liguo Jiao
AU - Jae Hyoung Lee
PY - 2026
DA - 2026/10/30
PB - arXiv
DO - 10.48550/arxiv.2610.41483
UR - https://arxiv.org/abs/2610.41483
AB - A polynomial optimization problem is said to have an SPLD structure if the polynomials defining its objective and constraints admit decompositions into separable and nonseparable parts, with the maximum degree of the separable parts exceeding that of the nonseparable parts. In this paper, we propose a bounded degree SDSOS hierarchy for globally solving a class of such problems. We establish the asymptotic convergence of this hierarchy over compact feasible sets and provide a sufficient condition for its finite convergence. Numerical experiments compare the proposed hierarchy with the BSDSOS hierarchy (Chuong et al. in J. Global Optim., 75(4):885-919, 2019).
ER -