Quantification of the mechanical behavior of normal and cancerous tissues has important implication in the diagnosis of breast tumor. The present work extends the authors' nonlinear elastography framework to incorporate the conventional X-ray mammography, where the projection of displacement information is acquired instead of full three-dimensional (3D) vector. The elastic parameters of normal and cancerous breast tissues are identified by minimizing the difference between the measurement and the corresponding computational prediction. An adjoint method is derived to calculate the gradient of the objective function. Simulations are conducted on a 3D breast phantom consisting of the fatty tissue, glandular tissue, and cancerous tumor, whose mechanical responses are hyperelastic in nature. The material parameters are identified with consideration of measurement error. The results demonstrate that the projective displacements acquired in X-ray mammography provide sufficient constitutive information of the tumor and prove the usability and robustness of the proposed method and algorithm.