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This paper studies a multi-UAV wireless network, in which multiple UAV users share the same spectrum to send individual messages to their respectively associated ground base stations (GBSs). The UAV users aim to optimize their locations to maximize the weighted sum rate. While most existing work considers simplified line-of-sight (LoS) or statistic air-to-ground (A2G) channel models, we exploit the location-specific channel knowledge map (CKM) to enhance the placement performance in practice. However, as the CKMs normally contain discrete site- and location-specific channel data without analytic model functions, the corresponding weighted sum rate function becomes non-differentiable in general. In this case, conventional optimization techniques relying on function derivatives are inapplicable to solve the resultant placement optimization problem. To address this issue, we propose a novel iterative algorithm based on the derivative-free optimization. In each iteration, we first construct a quadratic function to approximate the non-differentiable weighted sum rate under a set of interpolation conditions, and then update the UAVs' placement locations by maximizing the approximate quadratic function subject to a trust region constraint. Numerical results show the convergence of the proposed algorithm. It is also shown that the proposed algorithm achieves a weighted sum rate close to the optimal design based on exhaustive search with much lower implementation complexity, and it significantly outperforms the conventional optimization method based on simplified LoS channel models and the heuristic design with each UAV hovering above its associated GBS.