.png){kind=icon}
.png){kind=icon}
Return
The Moment-SOS hierarchy: Applications and related topics
.png){kind=icon}
OA
AI
J
DOI：10.1017/S0962492923000053.png)
.png){kind=icon}
Original request for help.png){kind=icon}
Share.png){kind=icon}
Save
Abstract
En 中文
The Moment-SOS hierarchy, first introduced in optimization in 2000, is based on the theory of the S-moment problem and its dual counterpart: polynomials that are positive on S. It turns out that this methodology can also be used to solve problems with positivity constraints 'f(x) >= 0 for all x is an element of S' or linear constraints on Borel measures. Such problems can be viewed as specific instances of the generalized moment problem (GMP), whose list of important applications in various domains of science and engineering is almost endless. We describe this methodology in optimization and also in two other applications for illustration. Finally we also introduce the Christoffel function and reveal its links with the Moment-SOS hierarchy and positive polynomials.
Keywords:
14Q30
44A60
90C22
90C23
42C05
47A57
49L25
Journal
IF:
11.3
Papers:
89
Citations:
3.4K
Organization
Cited Papers