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Planning a proper set of contact points on a given object/workpiece so as to satisfy a certain optimality criterion is a common problem in grasp synthesis for multifingered robotic hands and in fixture planning for manufacturing automation. In this paper, we formulate the grasp planning problem as optimization problems with respect to two grasp quality functions. For real-time computation, a simplified Min-analytic-center problem is proposed. Simulation and experimental results illustrate the validity of the proposed approach for optimal grasp planning.