# How to figure the initial guess to optimize

1. Dec 31, 2013

### PaulaS

I have the following problem to code using python:

I have 7 parameters: x,y,z,t, HF, M1F, and M2F. The user should input any of these 3 and the program should calculate the rest.

The relations that I have are:

HF = -xyt

M1F = -2xzt + 4yzt - xyt + 4tz^2

M2F = 2yzt - xyt

1 = -2xt + 2yt + 4zt

Attempt to solve the problem:

I have 7 parameters and the user should input 3 => I will be left with 4 parameters. So it's all about solving a system of 4 nonlinear equations with 4 unknowns.

I read online that scipy.optimize could be used to solve a system of nonlinear equations. But I need an initial guess.

Going back to the physics of the problem I have the following initial conditions:

x > 0

y > 0

z < 0

HF > 0

M1F > 0

M2F > 0

M2F > M1F (solving this inequality from the above equations I get: -x + y + 2z < 0)

HF > M1F + d (solving this inequality from the above equations I get: -x + 2y + 2z < 0)

How can these initial conditions help me get the initial guess so that I can solve my problem using scipy.optimize?

2. Dec 31, 2013

### Staff: Mentor

Did you test some trivial initial guesses, like +-1?

What is d in "HF > M1F + d"?

As y>0, "-x + y + 2z < 0" follows from "-x + 2y + 2z < 0", so (assuming those inequalities are correct) "M2F > M1F" follows from the last inequality.

3. Dec 31, 2013

4. Jan 9, 2014

### .Scott

I also haven't figured out the "d". I think it's a typo.
Another constraint: t > 0
If t is not provided, +1.0 would be as good a guess as any.