Lagrangian method for satisfiability problems of propositional calculus

Abstract

Hopfield type neural networks for solving difficult combinatorial optimization problems have used gradient descent algorithms to solve constrained optimization problems via penalty functions. However, it is well known that the convergence to local minima is inevitable in these approaches. Lagrange programming neural networks have been proposed. They differ from the gradient descent algorithms by using anti-descent terms in their dynamical differential equations. We analyze the stability and the convergence property of the Lagrangian method when it is applied to a satisfiability problem of propositional calculus.