Three optimization algorithms of generalized Lagrangian multiplier (GLM), interior point and modified sequence quadratic programming are proposed. By adopting a positive-negative-positive-negative-positive lens structure with a suitable aberration distribution and setting the reasonable and generally applicable parameters, the Gaussian structure of a full frame zoom lens with zoom range of 30-100 mm, constant F-number of 2.8, field-of-view angle of 24.421°-71.608° is obtained by the proposed three methods. These three optimization methods are analyzed and compared. The actual lens group is used to replace the Gaussian structure obtained by the GLM algorithm. The full spherical design is adopted and the obtained optimal design of the full-frame zoom lens meets the imaging requirements. Three zoom and compensation curves have good linearity, and the average value of the modulation transfer function of system is greater than 0.1 at 50 lp/mm. This full spherical design provides a good initial structure for the later aspheric optimal design.