Optimization technique based on Liapunov concepts

The principal aim of this paper is to present a new and unconventional approach for locating the equilibrium point of a real valued nonlinear objective function subject to nonlinear constraints. Most of the methods described in the literature depend on the fact that the stationary points of a function can be found by setting all the first derivatives to zero. In the method proposed here, the search is carried out on a positive-definite Liapunov Type of Function (LTF) of the gradients of a suitably modified objective function. By extending the concept of asymptotic stability of a discreté data control system, a search method is developed which ensures that the LTF progressively decreases in the direction of movement and eventually reaches a value of zero. This method provides an infallible and robust search technique for the solution of even highly complex nonlinear programming problems. © 1981.