Unified Spectral-LMI Constraint via Minimum Eigenvalue Embedding Operator
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| Natura: | Recurso digital |
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2026
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| _version_ | 1866902033832869888 |
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| author | Zhang, Jincheng |
| author_facet | Zhang, Jincheng |
| contents | <p><span>This paper proposes a novel unified constraint theory that couples and reconstructs linear matrix inequality (LMI) constraints and minimum eigenvalue constraints within the same spectral space. While the traditional LMI form F(x) = F0 + Σ xi Fi ⪰ 0 and the minimum eigenvalue constraint λ_min(A(x)) ≥ 0 are theoretically equivalent to semi-positive definite conditions, they suffer from a separation of expression in terms of optimization structure and numerical stability. This paper introduces a "spectral embedding operator" to construct a new unified constraint form, merging matrix positive definiteness and eigenvalue boundary control into a single operator inequality. This forms a new framework applicable to robust optimization, control system stability analysis, and machine learning constraint modeling.</span></p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_19637800 |
| institution | Zenodo |
| language | |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Unified Spectral-LMI Constraint via Minimum Eigenvalue Embedding Operator Zhang, Jincheng <p><span>This paper proposes a novel unified constraint theory that couples and reconstructs linear matrix inequality (LMI) constraints and minimum eigenvalue constraints within the same spectral space. While the traditional LMI form F(x) = F0 + Σ xi Fi ⪰ 0 and the minimum eigenvalue constraint λ_min(A(x)) ≥ 0 are theoretically equivalent to semi-positive definite conditions, they suffer from a separation of expression in terms of optimization structure and numerical stability. This paper introduces a "spectral embedding operator" to construct a new unified constraint form, merging matrix positive definiteness and eigenvalue boundary control into a single operator inequality. This forms a new framework applicable to robust optimization, control system stability analysis, and machine learning constraint modeling.</span></p> |
| title | Unified Spectral-LMI Constraint via Minimum Eigenvalue Embedding Operator |
| url | https://doi.org/10.5281/zenodo.19637800 |