Amplitude variation with offset (AVO) inversion has been widely used in reservoir characterization to predict lithology and fluids. However, some existing AVO inversion methods that use norm regularization may not obtain the block boundary of subsurface layers because the AVO inversion is a severely ill-posed problem. To obtain sparse and accurate solutions, we have introduced the minimization method as an alternative to norm regularization. We used minimization for simultaneous P- and S-impedance inversion from prestack seismic data. We first derived the forward problem with multiangles and set up the inversion objective function with constraints of a priori low-frequency information obtained from well-log data. Then, we introduced minimization of the difference of and norms, denoted as minimization, to solve this objective function. The nonconvex penalty function of the minimization method is decomposed into two convex subproblems via the difference of convex algorithm, and each subproblem is solved by the alternating direction method of multipliers. Compared to norm regularization, the results indicate that minimization has superior performance over norm regularization in promoting blocky/sparse solutions. Tests on synthetic and field data indicate that our method can provide sparser and more accurate P- and S-impedance inversion results. The overall results confirm that our method has great potential in the detection and identification of fluids.