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This article deals with the problem of real-time grasping force optimization for multifingered manipulation. Based on a review of existing approaches, the BHM and the HTL algorithms, a need for a strictly possible initial solution is found to be a common problem. Two approaches, the max-det approach and min-max approach, are proposed to resolve this problem. The first approach, although efficient in most cases, suffers from the problem of singularity. The latter can resolve the singularity problem, but is relatively slow compared with the former. The two approaches are combined in real implementations to efficiently compute a strictly initial solution, which is in turn used in the HTL algorithm (also the BHM algorithm). The whole algorithm is shown to be fast, fully automatic, and applicable to a wide class of manipulation tasks irrespective of the number of fingers and also the geometry of the manipulated objects. Experiments on the HKUST hand demonstrate the convergence and speed of the algorithm.