adding constraints to the objective function with svmtarin

I am working on a problem where I have two sets of data- say X (NxT) and Z(KxT). For each z(1xT), I want to classify those X' which are related to the z, from those (X-X') which are not. 1. I have prior information of a relationship binary matrix between Z and X (say C,NxK)), and 2. I know Z and X are negatively correlated. 3. I want to impose sparsity on the number of X' related to each z to reduce false positive I have formulated the problem as below -

where w is the weight of the classifier, lambda is the sparsity constant. I have used Matlab's svmtrain and svmclassify before on simple data but I am not sure how to add the constraints to the objective function and then use the two functions. Can someone please help me? Thanks!