The softassign quadratic assignment algorithm is a discrete-time, continuou
s-state, synchronous updating optimizing neural network. While its effectiv
eness has been shown in the traveling salesman problem, graph matching, and
graph partitioning in thousands of simulations, its convergence properties
have not been studied. Here, we construct discrete-time Lyapunov functions
for the cases of exact and approximate doubly stochastic constraint satisf
action, which show convergence to a fixed point. The combination of good co
nvergence properties and experimental success makes the softassign algorith
m an excellent choice for neural quadratic assignment optimization.