Abstract: In this study, under the Peak-to-Average Power Ratio (PAPR), energy, and binary (for antenna position selection) constraints, we proposed an antenna position selection and beam scanning method for colocated Multiple-Input Multiple-Output (MIMO) radar system using the min-max beampattern amplitude matching criterion. In our design, antenna positions and a set of probing waveforms were jointly determined to match a set of beampattern masks, and hence realize the beam scan. The resultant problem was large-scale, nonconvex, nonsmooth, and typical nondeterministic hard, because of the PAPR and nonconvex binary constraints, and the max and modulus operations in the objective function. To address these issues, we first transformed the min-max problem into the Iterative weighted Least Squares (ILS) problem using the Lawson algorithm, replaced the nonsmooth nonconvex objective function with the convex majorization function, and finally applied the alternating direction method of multipliers to solve the majorized ILS problem. Finally, several numerical examples were given to show the effectiveness of the proposed algorithms.