In addition to the noisy and limited spatial resolution characteristics of the electroencephalography (EEG) signal, the intrinsic nonstationarity in the EEG data makes the single-trial EEG classification an even more challenging problem in brain-computer interface (BCI). Variations of the signal properties within a session often result in deteriorated classification performance. This is mainly attributed to the reason that the routine feature extraction or classification method does not take the changes in the signal into account. Although several extensions to the standard feature extraction method have been proposed to reduce the sensitivity to nonstationarity in data, they optimize different objective functions from that of the subsequent classification model, and thereby, the extracted features may not be optimized for the classification. In this paper, we propose an approach that directly optimizes the classifier's discriminativity and robustness against the within-session nonstationarity of the EEG data through a single optimization paradigm, and show that it can greatly improve the performance, in particular for the subjects who have difficulty in controlling a BCI. Moreover, the experimental results on two benchmark data sets demonstrate that our approach significantly outperforms the compared approaches in reducing classification error rates.