Optimization by means of neural networks for combinatorial problems. On the Uesaka´s conjecture

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^tDHx, 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