Variational iteration method for solving optimization problems

Abstract

In this paper, we use variational iteration method (VIM) to solve some optimization problems. Exact solutions for many of the problems discussed in this paper are found. The main idea is to use both Euler's equations together with Lagrange multiplier in solving correction functionals

for the problems. We use He's VIM to handle many kinds of the variational problems, such as problems with fixed and moving boundaries, also, we solve some variational problems with extremals having corner points. Moreover, we found the solution of the variational problems involving conditional extremum such as, isoperimetric problems, via the variational iteration method. In addition, we introduced the relation between the conditional problems and the eigenvalue problems.