S-Lemma Based Unified Theory for Robust Linear Programming via LMIs

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1. Verfasser: Zhang, Jincheng
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Veröffentlicht: Zenodo 2026
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_version_ 1866902025934995456
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