In this paper, a general Maximum K-Min approach for classification is proposed. With the physical meaning of optimizing the classification confidence of the K worst instances, Maximum K-Min Gain/Minimum K-Max Loss (MKM) criterion is introduced. To make the original optimization problem with combinational constraints computationally tractable, the optimization techniques are adopted and a general compact representation lemma for MKM Criterion is summarized. Based on the lemma, a Nonlinear Maximum K-Min (NMKM) classifier and a Semi-supervised Maximum K-Min (SMKM) classifier are presented for traditional classification task and semi-supervised classification task respectively. Based on the experiment results of publicly available datasets, our Maximum K-Min methods have achieved competitive performance when comparing against Hinge Loss classifiers.