Based on the idea that the domains of attraction of all memorizad patterns must possess balanced shape,a minimax criterion for design of HoFfield associative memo-ry，which requires the smallest domain of attraction to be maximized，is proposed in this paper．A quick learning algorithm is first given，and furtherly，a constrained perception optimization algorithm is developed．A large number of simulation results confirm advan-tages of these algorithms given in this paper over existing ones．