How to figure the initial guess to optimize

[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?

 

[mfb]

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.

 

[AlephZero]

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

I already suggested that in a similar question, https://www.physicsforums.com/showthread.php?t=730426

But there was no follow up as to whether it worked.

 

[.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.

 

[LudusRex]

There are a few ways you could approach finding an initial guess for your optimization problem. One option is to use the initial conditions you have identified and use them as bounds for your parameters. For example, for x, you could set the lower bound as 0 and the upper bound as the maximum value of x based on your equations and initial conditions. Similarly, you could set bounds for y, z, and t based on the initial conditions you have identified.

Another option is to use a random search approach to generate initial guesses. This involves randomly generating values within the bounds you have identified and using those as initial guesses for your optimization algorithm. You can then run the optimization multiple times with different initial guesses and compare the results to see which one gives the best solution.

Additionally, you could use your knowledge of the physics of the problem to make an educated guess for the initial values. For example, you could set the initial values for x, y, and z based on the physical properties of the system or any known relationships between the variables.

Ultimately, the best approach for finding an initial guess will depend on the specific problem and the characteristics of your equations. It may be helpful to experiment with different methods and see which one gives the most accurate and efficient results.