Application of pontryagin's principle to bimodal optimization problems

Abstract

By using a version of the Pontryagin's principle allowing bimodal optimization, we formulate necessary optimality conditions and determine numerically the shape of optimal columns for two different problems. In all cases, we have to deal with bimodal optimization. The nonlinear system of differential equations is solved numerically. A first integral (Hamiltonian) is used to monitor the accuracy of integration. New numerical results are obtained, and comparison with some previously known cases is given, showing efficiency and accuracy of the suggested method. © 2007 Springer-Verlag.