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In this letter, we develop a family of approximate maximum-likelihood (ML) detectors for multiple-input multiple-output systems by relaxing the ML detection problem using constellation-specific polynomial constraints. The resulting constrained optimization problem is solved using a penalty function approach. Moreover, to escape from the local minima, which improves the detection performance, a differential equation algorithm using classical mechanics is proposed. Simulation results show that the polynomial constrained detector performs better than least-squares (LS) detector.