Symmetry groups, semidefinite programs, and sums of squares
Karin Gatermann,Pablo A. Parrilo +1 more
TLDR
The results, reinterpreted from an invariant-theoretic viewpoint, provide a novel representation of a class of nonnegative symmetric polynomials, termed “sum of squares matrices.”About:
This article is published in Journal of Pure and Applied Algebra.The article was published on 2004-09-01 and is currently open access. It has received 400 citations till now. The article focuses on the topics: Explained sum of squares & Sum-of-squares optimization.read more
Citations
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Book
Real Algebraic Geometry
TL;DR: The Tarski-Seidenberg Principle as a Transfer Tool for Real Algebraic Geometry as mentioned in this paper is a transfer tool for real algebraic geometry, and it can be used to solve the Hilbert's 17th Problem.
Journal ArticleDOI
Semidefinite programming relaxations for semialgebraic problems
TL;DR: It is shown how to construct a complete family of polynomially sized semidefinite programming conditions that prove infeasibility and provide a constructive approach for finding bounded degree solutions to the Positivstellensatz.
Journal ArticleDOI
Distributed average consensus with least-mean-square deviation
TL;DR: The problem of finding the (symmetric) edge weights that result in the least mean-square deviation in steady state is considered and it is shown that this problem can be cast as a convex optimization problem, so the global solution can be found efficiently.
Book ChapterDOI
Sums of Squares, Moment Matrices and Optimization Over Polynomials
TL;DR: This work considers the problem of minimizing a polynomial over a semialgebraic set defined byPolynomial equations and inequalities, which is NP-hard in general and reviews the mathematical tools underlying these properties.
Journal ArticleDOI
Complete search in continuous global optimization and constraint satisfaction
TL;DR: This survey covers the state of the art of techniques for solving general-purpose constrained global optimization problems and continuous constraint satisfaction problems, with emphasis on complete techniques that provably find all solutions (if there are finitely many).
References
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BookDOI
Introduction to mechanics and symmetry
TL;DR: A basic exposition of classical mechanical systems; 2nd edition Reference CAG-BOOK-2008-008 Record created on 2008-11-21, modified on 2017-09-27 as mentioned in this paper.
BookDOI
Singularities and groups in bifurcation theory
TL;DR: Singularities and groups in bifurcation theory as mentioned in this paper have been used to solve the problem of finding a group of singularities in a set of problems with multiple solutions.
Journal ArticleDOI
Global Optimization with Polynomials and the Problem of Moments
TL;DR: It is shown that the problem of finding the unconstrained global minimum of a real-valued polynomial p(x): R n to R, in a compact set K defined byPolynomial inequalities reduces to solving an (often finite) sequence of convex linear matrix inequality (LMI) problems.
DissertationDOI
Structured semidefinite programs and semialgebraic geometry methods in robustness and optimization
TL;DR: In this paper, the authors introduce a specific class of linear matrix inequalities (LMI) whose optimal solution can be characterized exactly, i.e., the optimal value equals the spectral radius of the operator.
Book
Linear Representations of Finite Groups
TL;DR: Representations and characters: generalities on linear representations character theory subgroups, products, induced representation compact groups examples.