Sum-of-squares chordal decomposition of polynomial matrix inequalities

DOI10.1007/s10107-021-01728-wOpenAlexW3044411208WikidataQ120721233 ScholiaQ120721233MaRDI QIDQ2689814

Yang Zheng, Giovanni Fantuzzi

Publication date: 14 March 2023

Published in: Mathematical Programming. Series A. Series B (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2007.11410

zbMATH Keywords

polynomial optimizationpolynomial matrix inequalitieschordal decomposition

Mathematics Subject Classification ID

Convex programming (90C25) Large-scale problems in mathematical programming (90C06) Sums of squares and representations by other particular quadratic forms (11E25) Forms of degree higher than two (11E76) Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) (12D15) Decomposition methods (49M27) Polynomial optimization (90C23)

Related Items (1)

Exploiting ideal-sparsity in the generalized moment problem with application to matrix factorization ranks

Uses Software

• YALMIP
• Mosek
• TSSOS

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A direct proof for the matrix decomposition of chordal-structured positive semidefinite matrices
• Positive semidefinite matrices with a given sparsity pattern
• Extremal psd forms with few terms
• Exploiting sparsity in semidefinite programming via matrix completion. II: Implementation and numerical results
• Symmetry groups, semidefinite programs, and sums of squares
• Uniform denominators in Hilbert's seventeenth problem
• Chordal decomposition in operator-splitting methods for sparse semidefinite programs
• A note on the representation of positive polynomials with structured sparsity
• Matrix sum-of-squares relaxations for robust semi-definite programs
• LMI relaxations in robust control
• Triangulated graphs and the elimination process
• Exploiting Sparsity in Semidefinite Programming via Matrix Completion I: General Framework
• An Introduction to Polynomial and Semi-Algebraic Optimization
• Robust Stability Analysis of Sparsely Interconnected Uncertain Systems
• Decomposition in Conic Optimization with Partially Separable Structure
• Non-commutative Real Algebraic Geometry - Some Basic Concepts and First Ideas
• Sparse SOS Relaxations for Minimizing Functions that are Summations of Small Polynomials
• Some NP-complete problems in quadratic and nonlinear programming
• Positive polynomials on semi-algebraic sets
• Scalable Design of Structured Controllers Using Chordal Decomposition
• Lasserre Hierarchy for Large Scale Polynomial Optimization in Real and Complex Variables
• Semidefinite Programming
• Pre- and Post-Processing Sum-of-Squares Programs in Practice
• LMI Techniques for Optimization Over Polynomials in Control: A Survey
• A New Sparse SOS Decomposition Algorithm Based on Term Sparsity
• TSSOS: A Moment-SOS Hierarchy That Exploits Term Sparsity
• Chordal-TSSOS: A Moment-SOS Hierarchy That Exploits Term Sparsity with Chordal Extension
• Exploiting Symmetries in SDP-Relaxations for Polynomial Optimization
• Inner Approximations for Polynomial Matrix Inequalities and Robust Stability Regions
• Sums of Squares and Semidefinite Program Relaxations for Polynomial Optimization Problems with Structured Sparsity
• Convergent SDP‐Relaxations in Polynomial Optimization with Sparsity

This page was built for publication: Sum-of-squares chordal decomposition of polynomial matrix inequalities