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First of all, I am a noob in optimization. I have the following problem:

I have the optimization vector x=(x1, x2, x3, x4, x5, x6). The cost function is:

min. (x3+x4)/x6

The constraints are: 

- quadratically equality constraints: e.g.: 
  k1*x5^2 + k2*x6 = k3*x5 + k4*x5 + k5*x1^2

- xmin < x < xmax

- some other linear constraints...

My biggest problem is to find a suitable solver for this problem. I already found the concept of Fractional Linear Programming by Boyd: https://web.stanford.edu/~boyd/cvxbook/bv_cvxslides.pdf (4-20)

However, it requires linear constraints. I also found heuristic methods to solve quadratic equality constrained problems: https://pdfs.semanticscholar.org/6008/57c54df025e732238425cf55f55997b4a67c.pdf https://web.stanford.edu/~boyd/papers/pdf/qcqp.pdf

However, I think they are not suitable to combine them with linear fractional programming.

I would be very glad if someone could mention any solution to this problem.

best regards Leo

I tried to linearize the constraints around different random points and took the result with the lowest costs. However, the solution does not fullfil the quafratic equallity constraints.

donjuedo
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Cleonidas
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  • Hello Cleonidas. Your question is well documented but I think that it is better to post it on https://math.stackexchange.com because your question seems to be mathematical ! Make a Paste/Copy from StackOverflow. – schlebe Sep 17 '19 at 15:02
  • This is a small problem. I would try a global solver like Baron or Couenne. Note that strict inequalities `xmin – Erwin Kalvelagen Sep 18 '19 at 15:04

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