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We study the problem of channel shortening in multicarrier modulation systems without training. We reformulate two existing methods, the sum-squared and the sum-absolute autocorrelation minimization algorithms (SAM and SAAM), into semidefinite programming to overcome their shortcoming of local convergence. We present the original SAM and SAAM cost functions into as a batch optimization problem before relaxing the original problem into globally convergent semidefinite programming algorithms. Our batch processor is superior to the original stochastic gradient algorithms in terms of achievable bit rate and signal to interference and noise ratio (SINR).