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We study constrained optimization of two-dwell serial acquisition schemes in this letter. A noncoherent detector with full-period correlation (FPC) is investigated. The mathematical problem is to minimize a cost function (the mean acquisition time) depending on four parameters (two dwell durations and two thresholds) with two constraints (the false alarm probability and the miss detection probability), which is a nonlinear mixed-integer programming (NLMIP) problem. The contribution of this letter is to simplify the expressions of the cost function and constraints, and to narrow the search range, so as to make the direct search method applicable to solve this NLMIP problem.