This letter is concerned with transmit and receive filter optimization for the K-user MIMO interference channel. Specifically, linear transmit and receive filter sets are designed which maximize the weighted sum rate while allowing each transmitter to utilize only the local channel state information. Our approach is based on extending the existing method of minimizing the weighted mean squared error (MSE) for the MIMO broadcast channel to the K-user interference channel at hand. For the case of the individual transmitter power constraint, however, a straightforward generalization of the existing method does not reveal a viable solution. It is in fact shown that there exists no closed-form solution for the transmit filter but simple one-dimensional parameter search yields the desired solution. Compared to the direct filter optimization using gradient-based search, our solution requires considerably less computational complexity and a smaller amount of feedback resources while achieving essentially the same level of weighted sum rate. A modified filter design is also presented which provides desired robustness in the presence of channel uncertainty.