Minimize kurtosis or skewness

HI all

Given x the weigths to give at each factor and 4 factor and a portfolio made from the 4 factor.

I'm searching a way to write in Matlab code a formula in order to minimize kurtosis using fmincon (Do you know other formula more useful?) and using as constraints skewness equal to A. Then I have to do vice versa: minimize skewness using as constraint kurtosis=b.

I have a 10,000*4 Data (each column is a factor).

Could you give me some hints on how I can write kurtsosis and skewness?

For example, I know for variance I can do f(x)=@(x) x'*COV*x where COV is the variance-covariance matrix and x are the weight to give to each factor. Is there a similar way to do it for skewness and kurtsosis? How can I write a variance constraints?

Thank you very much