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This letter proposes an antenna array synthesis technique based on simultaneous perturbation stochastic approximation (SPSA) for sparse linear arrays with multiple constraints. The constraints include the number of elements, the array aperture, and the minimum and the maximum distance between two adjacent elements. With a novel vector mapping between the element spacings and the variables of SPSA, the constrained optimization problem is simply transformed to a nonconstrained optimization problem, and the infeasible solutions are naturally avoided. Simulation results confirm the great efficiency and the robustness of the proposed method and show that our method can achieve better results with fewer numbers of elements than other existing methods. Moreover, based on this algorithm, the optimal thinning levels of sparse arrays are studied. The results may be used as a reference to the linear array design.