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Solving convex programming problems with equality constaints by neural networks. (English) Zbl 0941.90060

Summary: This paper presents a neural network approach for solving convex programming problems with equality constraints. After defining the energy function and neural dynamics of the proposed neural network, we show the existence of an equilibrium point at which the neural dynamics becomes asymptotically stable. It is shown that under proper conditions, an optimal solution of the underlying convex programming problems is an equilibrium point of the neural dynamics, and vice versa. The configuration of the proposed neural network with an exact layout is provided for solving linear programming problems. The operational characteristics of the neural network are demonstrated by numerical examples.

MSC:

90C25 Convex programming
68T05 Learning and adaptive systems in artificial intelligence
49M30 Other numerical methods in calculus of variations (MSC2010)
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