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

Minimizing 5-d discontinuous objective function - alternatives to N-M Simplex

  1. Aug 22, 2011 #1
    I am minimizing a scalar function of 5 variables which looks something like:
    f(x1,...x5) = -x1*x2, if g(x1,...x5)=1
    infinity, if g(x1,...x5)=0
    where g is can only take on two values, and cannot be expressed in closed-form.
    Because of the essential discontinuities in the domain, I figured I better try a derivative-free method like Nelder-Mead Simplex. I tried using the MATLAB fminsearch() implementation, and it is not performing too well. While it does converge (even for very low tolerances) it is not reaching the local minima. The function changes very little, if at all, between iterations. See the end of the post for a history of a typical optimization (first 30 iterations)
    Does anybody have any idea how to tune the simplex method for this problem, or suggest an alternative optimizer?

    Many thanks,

    s.

    Iteration Func-count min f(x) Procedure
    0 1 -0.00157673
    1 6 -0.00165556 initial simplex
    2 7 -0.00165556 reflect
    3 9 -0.00171195 expand
    4 11 -0.00172117 reflect
    5 13 -0.00188736 expand
    6 14 -0.00188736 reflect
    7 15 -0.00188736 reflect
    8 17 -0.00194533 reflect
    9 19 -0.00194533 contract inside
    10 21 -0.00214186 expand
    11 22 -0.00214186 reflect
    12 24 -0.00215877 reflect
    13 26 -0.00242805 expand
    14 28 -0.00272589 expand
    15 30 -0.00272589 contract inside
    16 31 -0.00272589 reflect
    17 33 -0.00272589 contract inside
    18 35 -0.00272589 contract inside
    19 37 -0.00274379 reflect
    20 39 -0.00274379 contract inside
    21 41 -0.00274379 contract inside
    22 43 -0.00274379 contract inside
    23 45 -0.00274379 contract inside
    24 47 -0.00274379 contract inside
    25 49 -0.00274379 contract inside
    26 51 -0.00274379 contract inside
    27 53 -0.00274379 contract inside
    28 55 -0.00274379 contract inside
    29 56 -0.00274379 reflect
    30 58 -0.00278432 reflect
    31 60 -0.00286262 reflect
    32 62 -0.00286262 contract inside
    33 63 -0.00286262 reflect
    34 65 -0.00292913 expand
    35 67 -0.00292913 contract inside
    36 69 -0.00305228 expand
    37 70 -0.00305228 reflect
    38 72 -0.00327878 expand
    39 73 -0.00327878 reflect
    40 75 -0.00356812 expand
     
  2. jcsd
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted



Similar Discussions: Minimizing 5-d discontinuous objective function - alternatives to N-M Simplex
  1. Minimal Function (Replies: 16)

Loading...