Lagrange-Type Neural Networks for Nonlinear Programming Problems with Inequality Constraints

By redefining multiplier associated with inequality constraint as a positive definite function of the originally-defined multiplier, u²i, =1,2,...,m, say, the nonnegative constraints imposed on inequality constraints in Karush-Kuhn-Tucker necessary conditions are removed completely. In the construction of Lagrange-type neural networks, it is no longer necessary to convert inequality constraints into equality constraints by slack variables in order to reuse those results concerned only with equality constraints. Utilizing this technique, a new Lagrange-type neural network is devised, which handles inequality constraints directly without adding slack variables. Finally, the local stability of the proposed Lagrange neural networks is analyzed rigourously with Liapunov’s first approximation principle, and its convergence is discussed with LaSalle’s invariance principle.