Nonnegativity constraints in numerical analysis. (English) Zbl 1192.65041

Chen, Donghui; Plemmons, Robert J.

Bultheel, Adhemar (ed.) et al., The birth of numerical analysis. Papers based on the presentations at the symposium, Leuven, The Netherlands, October 29–30, 2007. Hackensack, NJ: World Scientific (ISBN 978-981-283-625-0/hbk; 978-981-283-626-7/ebook). 109-139 (2010).

Summary: A survey of the development of algorithms for enforcing nonnegativity constraints in scientific computation is given. Special emphasis is placed on such constraints in least squares computations in numerical linear algebra and in nonlinear optimization. Techniques involving nonnegative low-rank matrix and tensor factorizations are also emphasized. Details are provided for some important classical and modern applications in science and engineering. For completeness, this report also includes an effort towards a literature survey of the various algorithms and applications of nonnegativity constraints in numerical analysis.
For the entire collection see [Zbl 1186.65003].

MSC:

65F20	Numerical solutions to overdetermined systems, pseudoinverses
65-03	History of numerical analysis
01A60	History of mathematics in the 20th century
65K05	Numerical mathematical programming methods
90C30	Nonlinear programming
94A08	Image processing (compression, reconstruction, etc.) in information and communication theory

Keywords:

historical survey; nonnegativity constraints; nonnegative least squares; matrix and tensor factorizations; image processing; algorithms; nonlinear optimization