Optimization problems in Matlab

Project members: 3

The aim of this project was to solve optimisation problems with differential equations as conditions using Lagrange functions. We compared, Explicit and Implicit Euler (using both fixed point iterations and Newton iterations) for drawing conclusions about their order of convergence and areas of stability.

Late on we study the Bernoulli-Euler equations

Which we can write (with variable substitution):

By approximating the second derivative with the second differential we get:

When implementing this in the equation systems above, interpreting D2U as a matrix vector multiplication and looking at the Lagrange function:

Which gives the equations:

In the full report, more details are showed and we show how the Lagrange function satisfy these equations. Furthermore we solve the specified beam problem in Matlab.

Full report (Swedish)