Globally converging hyperplanes for optimization

In this paper, we present a new cutting plane method, a variant of Kelley’s cutting plane method. Since the new algorithm, termed a globally cutting hyperplanes algorithm, can solve a nonlinear optimization program we are motivated in this work to present the theory and illustrations. Earlier, authors have reported another variant of Kelley’s cutting plane method termed a sharp-cut algorithm. The new algorithm too is based on successive linear programming principle and has a convergence rate at par with the sharp-cut algorithm. The new algorithm was also able to find multiple optimum solutions by varying a parameter in the algorithm. Two test examples are solved using the algorithm. We then solve a two-point boundary value problem using the new algorithm for the first time. A challenging nonlinear optimization problem from Hock and Schittkowsky (1981) is solved next. Lastly, an application example of profit maximization of an alkylation plant is presented.