Application of interior point method for optimization of characteristics of cargo ship with restricted service area

Abstract

The application of one of the modifications of the penalty function method (the interior point method) combined with the Kuhn-Tucker condition for optimization of characteristics of the cargo ship with restricted service area has been discussed. The expediency of renunciation of the classical penalty function method and the application of the interior point method associated with the introduction of slack variables is proved. Various ways of transforming the initial constrained extremal problem into the unconstrained one (solving the barrier problem) are considered. To solve the unconstrained optimization problem, the Newton method is used. Methods of the approximate determination of the Hessian matrix are discussed. Recommendations based on a large number of numerical experiments are given regarding the choice of coefficients used in the optimization algorithm. Recommendations on transforming the Lagrangian function if it is necessary are also given. The results of optimization calculations are given and analyzed.