Sums of Squares, Moment Matrices and Optimization Over Polynomials

By Monique Laurent. 2009

943 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/c33fa815e642e3f27c939f6c8f25c3313e6f2f56

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Theory and Mathematics

1. I. Itenberg
2. Viatcheslav Kharlamov
3. Eugenii Shustin
4. Ting Kei Pong
5. Jiawang Nie
6. Graziano Chesi
7. M. Seethharama Gowda
8. Paul Tseng

In Numerical Analysis

1. Ting Kei Pong
2. Jiawang Nie
3. Graziano Chesi
4. M. Seethharama Gowda
5. Paul Tseng
6. Bernard Mourrain
7. Alexander Kovacec
8. Carla Fidalgo

Citations in the corpus

• Optimality conditions and finite convergence of Lasserre’s hierarchy (2012, background): “However, if there are infinitely many global minimizers, the flat truncation condition is typically not satisfied (cf. Laurent [14, § 6.6]).”
• Polynomial complementarity problems (2016, background): “n. These generally involve SOS polynomials, certificates of positivity (known as positivestellensatz) and are related to some classical problems (example, Hilbert’s 17th problem) in algebraic geometry [11]. Our first result in this section gives the solvability for (individual) qs when f is copositive”
• LMI Techniques for Optimization Over Polynomials in Control: A Survey (2010, background): “In order to describe these techniques, let us introduce the following basic definitions (see, e.g., [6], [19], [20] for details).”
• Concepts and techniques of optimization on the sphere (2014, background): “, [14, 20, 21]) as well as the Bi-Quadratic Optimization problem over unit spheres (see, e.”
• A generalized flat extension theorem for moment matrices (2009, background): “In the multivariate case, M(y) is known as a generalized Hankel matrix (see [17]) or moment matrix (see [15]).”
• Positive semidefinite diagonal minus tail forms are sums of squares (2011, background): “Lasserre’s proof uses the ties existing between the theory of moments and sos representations, see [8] or [9].”
• Real algebraic geometry (2013, background): “Theorem 9 remains valid if one considers the action of the group of algebraic self-diffeomorphisms on the set of real infinitely near points, or more precisely, real curvilinear subschemes of given length of a rational surface [31].”
• Hankel Matrix Rank Minimization with Applications to System Identification and Realization (2013, background): “, yi corresponds to the ith monomial; see [27, 28].”