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(Q) transformation of R^n simplex to R^(n1)
Posted:
Jul 12, 1996 3:44 AM


I would like to have onetoone transformation of the open simplex in R^n
x_1 + x_2 + ... + x_n = 1 x_i > 0
to R^(n1).
This would help me to convert my constraint minimization problem to the nonconstraint one.
For example,
The open simplex in R^2 is a segment (0, 1). The logistic function
y = 1/(exp(x) + 1) inf < x < inf, 0 < y < 1
is a tranformation of R^1 (a line) to the open simplex (0, 1) (a segment) and it is not difficult to write reverse trasformation.
x = log(y/(1  y)) 0 < y < 1, inf < x < inf
My problem is that I don't know how it can be generalized to more dimensional cases.
Evgenii Rudnyi
 Chemistry Department rudnyi@comp.chem.msu.su rudnyi@mch.chem.msu.su Moscow State University http://www.chem.msu.su/people/rudnyi/welcome.html 119899 Moscow +(095)939 5452, fax+(095)932 8846, +(095)939 1205 Russia



