A neural resolution theory for optimization problems with constraints

This paper develops a new resolution theory for optimization problems by use of neural networks. The optimization problem is any non-linear one with constraint: an objective function is a non-linear function of real variables; the constraint is expressed as a non-linear equation among the variables. The neural network is a parallel information processing unit of the steepest descent method; it is modelled as a complex of a transformation system and a dynamical system. The theory presents sufficient conditions that the optimization problem should satisfy to be solved by use of the neural network. In addition, it establishes a construction method of the neural network from any given optimization problem that satisfies the sufficient conditions. [In Japanese.]