S-Lemma Based Unified Theory for Robust Linear Programming via LMIs
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2026
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| _version_ | 1866902025934995456 |
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| author | Zhang, Jincheng |
| author_facet | Zhang, Jincheng |
| contents | <p class="17"><span>This paper proposes a novel optimization theoretical framework that unifies the classical S-Lemma and Robust Linear Programming (RLP) into a single mathematical structure. Traditional RLP deals with the worst-case scenario of linear constraints under uncertain sets, while the S-Lemma provides the necessary and sufficient conditions for transforming quadratic inequality implications into linear matrix inequalities (LMIs). This paper constructs a "quadratic structure parameterized uncertainty matrix perturbation model," which allows robust linear constraints to be uniformly transformed into single solvable convex optimization conditions through the S-Lemma, resulting in a new unified equation system. This model theoretically extends the solvable boundary of robust optimization and structurally establishes a bridge between "linear constraints—quadratic uncertainty—LMI solvability."</span></p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_19568381 |
| institution | Zenodo |
| language | |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | S-Lemma Based Unified Theory for Robust Linear Programming via LMIs Zhang, Jincheng <p class="17"><span>This paper proposes a novel optimization theoretical framework that unifies the classical S-Lemma and Robust Linear Programming (RLP) into a single mathematical structure. Traditional RLP deals with the worst-case scenario of linear constraints under uncertain sets, while the S-Lemma provides the necessary and sufficient conditions for transforming quadratic inequality implications into linear matrix inequalities (LMIs). This paper constructs a "quadratic structure parameterized uncertainty matrix perturbation model," which allows robust linear constraints to be uniformly transformed into single solvable convex optimization conditions through the S-Lemma, resulting in a new unified equation system. This model theoretically extends the solvable boundary of robust optimization and structurally establishes a bridge between "linear constraints—quadratic uncertainty—LMI solvability."</span></p> |
| title | S-Lemma Based Unified Theory for Robust Linear Programming via LMIs |
| url | https://doi.org/10.5281/zenodo.19568381 |