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In this paper, we develop a family of approximate maximum likelihood (ML) detectors for multiple-input multiple-output (MlMO) systems by relaxing the ML detection problem. Polynomial constraints are formulated for any signal constellation. The resulting relaxed constrained optimization problem is solved using a penalty function approach. Moreover, to escape from the local minima and to improve the performance of detection, a probabilistic restart algorithm based on noise statistics is proposed. Simulation results show that our polynomial constrained detectors perform better than several existing detectors.