how to optimize a function ( 6 independent variables) which is not smooth but has rough minimum point

Dear fellows,

I have asked this question before in a previous post http://www.mathworks.co.uk/matlabcentral/answers/129592-how-to-optimize-a-function-which-is-no-smooth-but-has-rough-minimum-point

But now I realize though those replies do help in the case with only variable, they could not solve my problem. But in my problem, the function f contains 6 variables. And I want to minimize the function through the 6 variables? Could you offer me some advice please?

Thanks, Xueqi

[Matt J]

How is the situation critically different now that you have 6 variables, exactly? The general advice there was to smooth the surface. In particular, Alan Weiss' recommendation that you convolution-smooth the function can still be done in 6 dimensions.

[xueqi]

Thank you. I just do not quite understand how to do it exactly. I have two major problems.

• How to decide the range of the variables to be integrated. Alan suggested that take g(x) = int(f(t),x-0.5,x+0.5).I can not just take from x-0.5 to x+05. These variables are constrained, doing so would violate the constraints. Despite the problem of constraints, what is a proper range to be enough to smooth the function?
• How to write the multiple integration? Denote the function as f(x1,x2,x3,x4,x5,x6). Could you show me how to correctly write the integration code?