With such high dimensions and with that many training samples you will require a lot of memory to use any popular implementation of SVM. If I were to face this problem then I would consider at least one of these options:
- Reduce the dimension of each vector, there are plenty of algorithms to do this but PCA is a good start.
- Get computing time in some host with a lot of memory (maybe one of amazon ec2 instances would be suffice)
- Test with a linear online approximation of SVM. In high dimensions, it is very likely that you can separate the classes linearly and there are SVM online approximations that you could use and then load to memory just one sample at a time in which case you don't need as much memory (I would consider pegasos-svm for this).