an:05507018
Zbl 1163.13021
Laurent, Monique
Sums of squares, moment matrices and optimization over polynomials
EN
Putinar, Mihai (ed.) et al., Emerging applications of algebraic geometry. Papers of the IMA workshops Optimization and control, January 16--20, 2007 and Applications in biology, dynamics, and statistics, March 5--9, 2007, held at IMA, Minneapolis, MN, USA. New York, NY: Springer (ISBN 978-0-387-09685-8/hbk). The IMA Volumes in Mathematics and its Applications 149, 157-270 (2009).
2009
a
13P10 13J25 14P10 15A99 90C22 90C30
positive polynomial; moment problem; polynomial optimization; semidefinite programming
The author considers the problem of minimizing a polynomial over a semialgebraic set defined by polynomial equations and inequalities. He presents these hierarchies of approximations and their main properties, and then reviews the mathematical tools underlying these properties. The paper contains sections of Positive polynomials and sums of squares; Moment sequences and moment matrices; Back to the polynomial optimization problem; Application to optimization and Exploiting algebraic structure to reduce the problem size.
For the entire collection see [Zbl 1151.14004].
Yueh-er Kuo (Knoxville)