# Numerically find minimum of 2 dimensional surface

I have a large equation that essentially takes two variables and returns a real number. I know that the two values are real numbers between 0 and 10. Is there a standard way to numerically find the minimum point on the surface?

I'm multiplying two Poisson distributions together to get the probability of two independent events happening. I have some real world data that I'm trying to model and am trying to find the two lambda values for the distribution that best models that real world data.

I have a cost function that gives a cost for any specific two lambdas and am trying to find the 2 values that minimize that cost.

So the equation is more or less the sum of[((two poisson distributions multiplied together) - (some value measured from the real workd))^2]

I'm trying to find the two lambda values that give the minimum for this function.

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Assuming that you do not have an a.e. differentiable function, do you know that you have a continuous function? If not, can you describe the region on which it is not continuous? If not, then the task may be hopeless. Can you provide any information about this function? Perhaps this formula that you mention? – alex.jordan Dec 10 '12 at 9:32
Assuming your function is differentiable, a minimum in the interior of your region is a critical point, i.e. the partial derivatives with respect to $x$ and $y$ are both $0$. There may be many critical points, though, and not all will be minima. You might start by graphing and trying to locate the minimum approximately. Then use numerical methods to solve the system of two equations in two unknowns in a region small enough that the only critical point in it is the minimum. – Robert Israel Dec 10 '12 at 10:00
If you post the equation of the surface then some one can obtain more information and most probably you'll get a good answer. – the_candyman Dec 10 '12 at 10:39