In this paper, the possibility of synthesizing a linear antenna array for multiple objectives with the thinning approach is demonstrated. The thinning space is constrained to three cases (side, central, and random) parts instead of a fully filled linear array. In the case of the side part, a set of elements located on both edges of the array are removed with the optimized elements close to the center remaining unchanged. As in the case of the central part, only a set of elements close to the center are removed. In the case of a random selection of elements, the cancellation process is carried out randomly within the sides and the center. Since the amplitude weights of the elements located on the edges of the array have a small amplitude excitation, the method of side thinning gives better results than the other two cases. Moreover, in cases of side and random thinning, the last element of each side is excluded from the thinning process to maintain the aperture size. The convex algorithm (CA) is used to perform such thinning optimization. CA optimization efficiently computes a multi-objective function in coordination with the thinned array technique, such as preserving the main beamwidth in all cases with the reduction of sidelobe levels, generating one or more nulls, and steering the main beam in a certain direction. The simulation results, in all cases, show that 30%-40% of the array elements can be turned off with achieving a multi-objective radiation pattern.