The \(\mathcal{S}\)-cone and a primal-dual view on second-order representability

DOI10.1007/s13366-020-00512-9zbMath1471.90111arXiv2003.09495OpenAlexW3041133009MaRDI QIDQ2022366

Helen Naumann, Thorsten Theobald

Publication date: 29 April 2021

Published in: Beiträge zur Algebra und Geometrie (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2003.09495

zbMATH Keywords

second-order conepositive polynomialsdual cone\(\mathcal{S}\)-conearithmetic-geometric exponentialssums of non-negative circuit polynomials

Mathematics Subject Classification ID

Semidefinite programming (90C22) Convex programming (90C25) Semialgebraic sets and related spaces (14P10) Convex sets in (n) dimensions (including convex hypersurfaces) (52A20) Forms over real fields (11E10) Polynomial optimization (90C23)

Related Items

Sublinear circuits for polyhedral sets, Symmetry Reduction in AM/GM-Based Optimization, Sublinear circuits and the constrained signomial nonnegativity problem

Uses Software

• REPOP

Cites Work

• Amoebas, nonnegative polynomials and sums of squares supported on circuits
• Forms derived from the arithmetic-geometric inequality
• Lectures on Modern Convex Optimization
• Relative Entropy Relaxations for Signomial Optimization
• Optimal Size of Linear Matrix Inequalities in Semidefinite Approaches to Polynomial Optimization
• A unified framework of SAGE and SONC polynomials and its duality theory
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