<p>Person re-identification is a challenging task to identify the same person among disjoint camera views. Recently, many deep learning approaches such as architecture based on mixed distance maximization have been proposed, but person re-identification still is suffered from the local optima problem resulted from training strategies and limits of datasets etc. We design a new objective function, which is constructed of local and global objective function based on the full-triple relation unlike the previous version using only two edges of triangle in a set of triplet units. First, we define a local objective function to achieve maximization of intra-distance inside a triplet. Second, we also define a global objective function to take account of distances between triplets. Finally, we propose a main objective function based on two distances in order to take full advantage of the information of triplets. We define this main objective function based on the combination of two distances. This combination of two distances is also called as a mixed distance based on the full-triple relation, which makes the distances between triplets increase and the distances between the matched pairs in each triplet decrease. Our deep learning framework is validated through several datasets and quantitative comparisons to the-state-of-the-art methods and demonstrate that it has potentially more discriminative and more efficient performance for person re-identification.</p>