Multi-dimensional optimization / root search algorithm / something

Question

I have five values: A, B, C, D, and E.

Given the restriction A + B + C + D + E = 1 and the five functions F (A), F (B), F (C), F (D), F (E), I need to solve for A from E such that that F (A) = F (B) = F (C) = F (D) = F (E).

What is the best algorithm / approach to use? I don’t care if I need to write myself, I just wanted to know where to look.

EDIT: These are non-linear functions. In addition, they cannot be characterized. Some of them can be subsequently interpolated from the data table.

Answer 1

. , , . , .

• , Newton-Raphson
• .
• F (, ), Bisection, .

, , .

Answer 2

, . , , .

min k
.
A + B + C + D + E = 1
F1 (A) - k = 0
F2 (B) - k = 0
F3 (C) -k = 0
F4 (D) - k = 0
F5 (E) -k = 0

, ,

min k + mu * sum (Fi (x_i) - k) ^ 2
A + B + C + D + E = 1

SQP .

, .

Answer 3

. , . , , :

1) A = B = C = D = E = 1/5
2) F1 (A) F5 (E) A E , , 5 (). 3) A-E , 1 F1-F5.
4) , .

- . , 5 2.

Answer 4

A + B + C + D + E = 1
F(A) = F(B) = F(C) = F(D) = F(E)

A, B, C, D E 1/5. , , ...

(!)

, F1 (A) = F2 (B) = F3 (C) = F4 (D) = F5 (E), - (. Martijn). , E = 1 - A - B - C - D. 4x4. - , , . - , , , .

, , .

Answer 5

ALGENCAN ( TANGO) . Python.

http://www.ime.usp.br/~egbirgin/tango/codes.php - " , , , . ..."

http://pypi.python.org/pypi/TANGO%20Project%20-%20ALGENCAN/1.0

Answer 6

Google OPTIF9 ALLUNC. .

Answer 7

, . , .

, A, B, C, D, 1-E = A + B + C + D.

-, F (A) = F (B) = F (C) = F (D), A. F (A), B, C, D . , , , A + B + C + D <= 1.

, .

Answer 8

Swarm Particle. . . Wiki .