The softassign quadratic assignment algorithm is a discrete-time, contin- uous-state, synchronous updating optimizing neural network. While its effectiveness has been shown in the traveling salesman problem, graph matching, and graph partitioning in thousands of simulations, its con- vergence properties have not been studied. Here, we construct discrete- time Lyapunov functions for the cases of exact and approximate dou- bly stochastic constraint satisfaction, which show convergence to a fixed point. The combination of good convergence properties and experimen- tal success makes the softassign algorithm an excellent choice for neural quadratic assignment optimization.
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