In multiple-input multiple-output radar, to localize a target and estimate its reflection coefficient, a given cost function is usually optimized over a grid of points. The performance of such algorithms is directly affected by the grid resolution. Increasing the number of grid points enhances the resolution of the estimator but also increases its computational complexity exponentially. In this work, two reduced complexity algorithms are derived based on Capon and amplitude and phase estimation (APES) to estimate the reflection coefficient, angular location and, Doppler shift of multiple moving targets. By exploiting the structure of the terms, the cost-function is brought into a form that allows us to apply the two-dimensional fast-Fourier-transform (2D-FFT) and reduce the computational complexity of estimation. Using low resolution 2D-FFT, the proposed algorithm identifies sub-optimal estimates and feeds them as initial points to the derived Newton gradient algorithm. In contrast to the grid-based search algorithms, the proposed algorithm can optimally estimate on- and off-the-grid targets in very low computational complexity. A new APES cost-function with better estimation performance is also discussed. Generalized expressions of the Cramér-Rao lower bound are derived to asses the performance of the proposed algorithm.