Abstract
A novel two-phase neural network that is suitable for solving a large class of constrained or unconstrained optimization problem is presented. For both types of problems with solutions lying in the interior of the feasible regions, the phase-one structure of the network alone is sufficient. When the solutions of constrained problems are on the boundary of the feasible regions, the proposed two-phase network is capable of achieving the exact solutions, in contrast to existing optimization neural networks which can obtain only approximate solutions. Furthermore, the network automatically provides the corresponding Lagrange multiplier associated with each constraint. Thus, for linear programming, the network solves both the primal problems and their dual problems simultaneously.
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