Optimization by means of neural networks for combinatorial problems. On the Uesaka's conjecture - Nishi, T.; Imai, K. (1997 IEEE International Symposium on Circuits and Systems, 2002)
This paper shows the possibility that, as the Uesaka's conjecture states, the globally optimum solution (not a local minimum solution) of a kind of combinatorial problem represented by a quadratic function may be obtained by solving a differential equation. For this purpose we consider a class of objective functions, f(x)=H/sup t/DHx, where H is an Hadamard matrix and D a diagonal matrix. Furthermore, we extend the above class of functions to more general class of functions. Thus the result seems to support that the Uesaka's conjecture may hold true.