Curve Enclosing Max Area

1. Dec 30, 2009

ozlegolas

1. The problem statement, all variables and given/known data
Hi all,
I have a project for optimization class and the problem is that:

A curve $$\alpha$$(t) = (x(t),y(t)) of length L = 6 units is to be found so that the area enclosed by the curve and the x-axis is maximum. Curve will be start at (1, 0) and end at (3, 0).

I am supposed to solve this problem by using various kind of optimization algorithms which are Steepest descent, Newton’s method, Fletcher-Reeves and Davidon-Fletcher-Powell. I'll apply these methods in Matlab.

3. The attempt at a solution

Since these methods are for unconstrained optimization problems, I think I should treat this constrained problem as an unconstrained problem using some methods like penalty and barrier methods. However, I could't find out which method I should apply.