Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Software to solve Nonlinear Systems (ineq and eq)

  1. Jan 14, 2013 #1
    Hi everyone,

    I've got an optimisation/computing question. I have a system of nonlinear equalities and inequalities, which I've written below for reference. It's the conditions for a minimiser of a Karush-Kuhn-Tucker problem. Would anyone be kind enough to explain how I could use software to compute the solution? I've never really used matlab or maple which I assume might be able to do that. A second best would be computing the solution to the original problem, which I've also posted.

    Ideally I would like to compute solutions to these, which I hope are the KKT conditions for a minimiser

    [itex]2s_{1}-\mu_{1}+\lambda_{1}(\frac{5}{2}(\frac{1}{2}s_{1}+
    \frac{1}{4}s_{2}+\frac{1}{4})^{4}-1)+\lambda_{2}(\frac{2}{3}
    (\frac{1}{3}s_{1}+\frac{1}{3}s_{2}+\frac{1}{3}))=0[/itex]

    [itex]2s_{2}-\mu_{2}+\lambda_{1}(\frac{5}{4}(\frac{1}{2}s_{1}+
    \frac{1}{4}s_{2}+\frac{1}{4})^{4})+\lambda_{2}
    (\frac{2}{3}(\frac{1}{3}s_{1}+\frac{1}{3}s_{2}+
    \frac{1}{3})-1)=0[/itex]

    [itex](\frac{1}{2}s_{1}+\frac{1}{4}s_{2}+\frac{1}{4})^{5}-s_{1}=0[/itex]
    [itex](\frac{1}{3}s_{1}+\frac{1}{3}s_{2}+\frac{1}{3})^{2}-s_{2}=0[/itex]

    [itex]s_{1},s_{2} \geq 0[/itex]
    [itex]\mu_{1},\mu_{2} \geq 0[/itex]

    [itex]\mu_{1}s_{1}=0[/itex]
    [itex]\mu_{2}s_{2}=0[/itex]

    If that seems a bit unlikely or difficult a second best would be just computing the solution to the original problem which is:

    minimise [itex]s_{1}^{2}+s_{2}^{2}[/itex]
    such that
    [itex](\frac{1}{2}s_{1}+\frac{1}{4}s_{2}+\frac{1}{4})^{5}-s_{1}=0[/itex]
    [itex](\frac{1}{3}s_{1}+\frac{1}{3}s_{2}+\frac{1}{3})^{2}-s_{2}=0[/itex]

    Many thanks,

    Peter
     
  2. jcsd
  3. Jan 16, 2013 #2
    Anyone? Thoughts appreciated!
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook