Minimizing discontinuous 5-dfunction using fminsearch()

Hi all,

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 (fminsearch). It is not performing very 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. Does anybody have any idea how to adjust fminsearch() for this problem, or suggest an alternative optimizer?

Many thanks,

s.

EDIT: I think the problem might be that the discontinuity occurs very close to the stationary point, which fminsearch() reportedly does not handle well. Any ideas about how to solve this?

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