1 citations · 1 across the 10 of their papers we have counts for
11 papers
Convergence rate of the moment-SOS hierarchy for univariate polynomial optimization
Didier Henrion, Mohab Safey El Din
We study the convergence rate of the moment-SOS (sum-of-squares) hierarchy for polynomial optimization problems (POPs) on a bounded subset of the real line described by arbitrary p…
Polynomial-Based Solutions to Targeting Problems for Onboard Applications
Adam Evans, Alberto Fossa, Roberto Armellin +2
This paper solves the targeting problem focusing on accuracy, computational efficiency, and reliability. The trajectory optimization problem is first recast as a polynomial optimiz…
Extreme points and faces in the moment problem
Didier Henrion, Martin Kružík, Stephan Weis
The polyconvex envelope, used in the calculus of variations and elasticity theory, was expressed by Dacorogna pointwise as a linear program on finitely atomic measures on the space…
Composition and tensor train structure in polynomial optimization
Llorenç Balada Gaggioli, Didier Henrion, Milan Korda
We study polynomial optimization problems whose objective has a composition or tensor train structure. These polynomials can be evaluated as a sequence of maps, giving rise to inte…
Mollified Christoffel-Darboux Kernels and Density Recovery on Varieties
Leandro Bentancur, Didier Henrion, Mauricio Velasco
We introduce mollified Christoffel-Darboux (CD) kernels on varieties, a systematic regularization of the classical CD kernel associated with a probability measure on a compact doma…
Solving Stengle's Example in Rational Arithmetic: Exact Values of the Moment-SOS Relaxations
Didier Henrion
We revisit Stengle's classical univariate polynomial optimization example whose constraint description is degenerate at the minimizers. We pro…
Density, Determinacy, Duality and a Regularized Moment-SOS Hierarchy
Didier Henrion
The standard moment-sum-of-squares (SOS) hierarchy is a powerful method for solving global polynomial optimization problems. However, its convergence relies on Putinar's Positivste…
Positively not SOS: pseudo-moments and extreme rays in exact arithmetic
Didier Henrion
A polynomial that is a sum of squares (SOS) of other polynomials is evidently positive. The converse is not true, there are positive polynomials which are not SOS. This note focuse…
Polyconvex double well functions
Didier Henrion, Martin Kružík
We investigate polyconvexity of the double well function for given matrices . Such functions are fundamental in the…
Maximal entropy in the moment body
Didier Henrion
A moment body is a linear projection of the spectraplex, the convex set of trace-one positive semidefinite matrices. Determining whether a given point lies within a given moment bo…
Infinite-dimensional Christoffel-Darboux polynomial kernels on Hilbert spaces
Didier Henrion
In these notes, the Christoffel-Darboux polynomial kernel is extended to infinite-dimensional Hilbert spaces, following as closely as possible its original finite-dimensional treat…