Aiming at the influence of camera calibration error and robot positive kinematics solution error on the handeye calibration accuracy, and the handeye calibration is susceptible to external interference and a large error is produced when singular value decomposition is used in traditional dual quaternion method, an optimized dual quaternion handeye calibration algorithm was proposed.In this algorithm, the handeye calibration equation was decomposed into two parts in the form of dual quaternion, to simplify the problem model, and to estimate the rotation matrix and translation vector respectively; the linear matrix inequality optimization method was used to replace the traditional singular value decomposition method to obtain a more accurate rotation matrix, then the calibration equation of the translation vector was rewrote to establish a new objective function, and then the linear matrix inequality optimization method was used to obtain the translate vector.Finally, through analyzing the test results of the open source data set experiment and the actual measurement experiment on the handeye calibration platform, it is proved that the algorithm is superior to the traditional dual quaternion (CDQ) algorithm, the classic Tsai algorithm and the Navy algorithm in terms of accuracy and stability, the feasibility of the algorithm is verified in practical applications.