Darwin–Radau equation

A posynomial is a function of the form

$f(x_1,x_2,\dots ,x_n)=\sum _{k=1}^K{c}_k{x}_1^{a_{1k}}\cdots x_n^{a_{nk}}$

where all the coordinates $x_i$ and coefficients $c_k$ are positive real numbers, and the exponents $a_{ik}$ are real numbers. Posynomials are closed under addition, multiplication, and nonnegative scaling.

For example,

$f(x_1,x_2,x_3)=2.7x_1^2{x}_2^{-1/3}{x}_3^{0.7}+2x_1^{-4}{x}_3^{2/5}$

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