The twin support vector machines(TWSVMs) and the recently proposed variant models are all designed to solve two dual quadratic programming problems(QPPs) with constraint conditions independently in high dimensional space. However, since each dual QPP involves a set of dual variables with its size determined by the number of samples of other classes, when we need to cope with large-scaled datasets, the method of directly solving QPP will lead to very high computational complexity. Therefore, this paper proposes an improved twin support vector machine model, known as a fixed-point TWSVM(FP-TWSVM). This model transforms the traditional TWSVM and its variant models into a series of unimodal function optimization problems in one-dimensional space. Efficient linear search methods are used such as Fibonacci algorithm and golden section method to solve these one-dimensional unimodal function optimization problems. The validity of FP-TWSVM algorithm is verified by numerical experiments on several datasets including large datasets. The experimental results show that the FP-TWSVM has faster training speed and consumes less memory space while maintaining vertically the same classification accuracy as other models.