Tensor decompositions (e.g., higher-order analogues of matrix decompositions such as the singular value decomposition) are powerful tools for data analysis. In particular, the CANDECOMP/PARAFAC (CP) model has proved useful in many applications such chemometrics, signal processing, and web analysis, to name a few. The problem of computing the CP decomposition is a nonlinear optimization problem and typically solved using an alternating least squares approach. We discuss the use of (non-alternating) optimization-based algorithms for CP, including how to compute the derivatives necessary for the optimization methods. Numerical studies highlight the positive features of our CPOPT algorithms, as compared with alternating least squares and nonlinear least squares approaches. We present applications to predicting links in bibliometric data. This is joint work with Evrim Acar and Daniel M. Dunlavy.