Darwin–Radau equation: Difference between revisions
Jump to navigation
Jump to search
en>Bibcode Bot m Adding 1 arxiv eprint(s), 0 bibcode(s) and 0 doi(s). Did it miss something? Report bugs, errors, and suggestions at User talk:Bibcode Bot |
en>Yobot m →References: WP:CHECKWIKI error fixes - Replaced endash with hyphen in sortkey per WP:MCSTJR using AWB (9100) |
||
| Line 1: | Line 1: | ||
A '''posynomial''' is a [[function (mathematics)|function]] of the form | |||
: <math>f(x_1, x_2, \dots, x_n) = \sum_{k=1}^K c_k x_1^{a_{1k}} \cdots x_n^{a_{nk}}</math> | |||
where all the coordinates <math>x_i</math> and coefficients <math>c_k</math> are positive [[real number]]s, and the exponents <math>a_{ik}</math> are real numbers. Posynomials are closed under addition, multiplication, and nonnegative scaling. | |||
For example, | |||
: <math>f(x_1, x_2, x_3) = 2.7 x_1^2x_2^{-1/3}x_3^{0.7} + 2x_1^{-4}x_3^{2/5}</math> | |||
is a posynomial. | |||
Posynomials are not the same as [[polynomial]]s in several independent variables. A polynomial's exponents must be non-negative integers, but its independent variables and coefficients can be arbitrary real numbers; on the other hand, a posynomial's exponents can be arbitrary real numbers, but its independent variables and coefficients must be positive real numbers. This terminology was introduced by [[Richard Duffin|Richard J. Duffin]], Elmor L. Peterson, and [[Clarence Zener]] in their seminal book on [[Geometric programming]]. | |||
These functions are also known as "'''posinomials'''" in some literature. | |||
==References== | |||
*{{cite book | |||
| author = Richard J. Duffin | |||
| coauthors = Elmor L. Peterson, Clarence Zener | |||
| title = Geometric Programming | |||
| publisher = John Wiley and Sons | |||
| date = 1967 | |||
| pages = 278 | |||
| isbn = 0-471-22370-0 | |||
}} | |||
*{{cite book | |||
| author = Stephen P Boyd | |||
| coauthors = Lieven Vandenberghe | |||
| title = Convex optimization ([http://www.stanford.edu/~boyd/cvxbook/ pdf version]) | |||
| publisher = Cambridge University Press | |||
| date = 2004 | |||
| pages = | |||
| isbn = 0-521-83378-7 | |||
}} | |||
*{{cite book | |||
| author = Harvir Singh Kasana | |||
| coauthors = Krishna Dev Kumar | |||
| title = Introductory operations research: theory and applications | |||
| publisher = Springer | |||
| date = 2004 | |||
| pages = | |||
| isbn = 3-540-40138-5 | |||
}} | |||
* D. Weinstock and J. Appelbaum, "Optimal solar field design of stationary collectors," J. of Solar Energy Engineering, 126(3):898-905, Aug. 2004 http://dx.doi.org/10.1115/1.1756137 | |||
==External links== | |||
* S. Boyd, S. J. Kim, L. Vandenberghe, and A. Hassibi, [http://www.stanford.edu/~boyd/gp_tutorial.html A Tutorial on Geometric Programming] | |||
{{mathapplied-stub}} | |||
[[Category:Mathematical optimization]] | |||
Revision as of 15:59, 20 April 2013
A posynomial is a function of the form
where all the coordinates and coefficients are positive real numbers, and the exponents are real numbers. Posynomials are closed under addition, multiplication, and nonnegative scaling.
For example,
is a posynomial.
Posynomials are not the same as polynomials in several independent variables. A polynomial's exponents must be non-negative integers, but its independent variables and coefficients can be arbitrary real numbers; on the other hand, a posynomial's exponents can be arbitrary real numbers, but its independent variables and coefficients must be positive real numbers. This terminology was introduced by Richard J. Duffin, Elmor L. Peterson, and Clarence Zener in their seminal book on Geometric programming.
These functions are also known as "posinomials" in some literature.
References
- 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.
My blog: http://www.primaboinca.com/view_profile.php?userid=5889534
- 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.
My blog: http://www.primaboinca.com/view_profile.php?userid=5889534
- 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.
My blog: http://www.primaboinca.com/view_profile.php?userid=5889534
- D. Weinstock and J. Appelbaum, "Optimal solar field design of stationary collectors," J. of Solar Energy Engineering, 126(3):898-905, Aug. 2004 http://dx.doi.org/10.1115/1.1756137
External links
- S. Boyd, S. J. Kim, L. Vandenberghe, and A. Hassibi, A Tutorial on Geometric Programming