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How to formulate nonlinear optimization problem with large number of variables and constraints

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Karl Burkamp
Karl Burkamp on 18 May 2021
Answered: Alan Weiss on 20 May 2021
Hello,
i have a problem formulating a nonlinear optimization problem with matlab and don't really know how to start or if i go the right approach.
I have a nonlinear equation looking like
with total of 10 variables --> x()
Then i have about 500 constraints with the same equation as above with fixed but different k, const.a, const.b and const.c.
I want to optimize so that i have best values for x(1) to x(10) to have best possible solution for k when inserting different const.a b and c.
Will the optimizer handle the fact that the expression in the log should not be negative? or does that have to be a constraint as well?
What is the best way to formulate it for the optimizer? I am even not sure if i described my problem properly.
I use Matlab 2019b
Best regards
Karl
  2 Comments
Karl Burkamp
Karl Burkamp on 20 May 2021
Hey Alan,
thanks for quick response.
Sorry if i did not express my problem properly.
I have a nonlinear equation like the one given above for that i hope will fit my Data in some way. I have 500 datasets for k, a, b and c. I now want to optimize x(1) to x(10) to fit all datasets k, a, b, c in the best way. So in the end i want to have the equation seen above --> k as function of a, b and c with best fitted constants x(1) to x(10).
Best regards
Karl

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Answers (1)

Alan Weiss
Alan Weiss on 20 May 2021
It sounds to me as if you want to fit an expression to data, possibly in a least-squares sense. For examples and details, see Nonlinear Least Squares (Curve Fitting). Maybe these examples from that section will help in some way: Nonlinear Least-Squares, Problem-Based, Nonlinear Data-Fitting Using Several Problem-Based Approaches, Nonlinear Data-Fitting, or Nonlinear Curve Fitting with lsqcurvefit.
Good luck,
Alan Weiss
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