Homework #2
Assigned: Jan. 13th, 2010
Due: Jan. 21st, 2010
Points: 20

1. 10 points
   minimize f = x1 + x2^2 + x2*x3 + 2*x3^2 with respect to {x1, x2, x3} subject to h = x1^2 + x2^2 + x3^2 - 1 = 0. Obtain a solution using the necessary and sufficient conditions. Is the solution unique?
2. 10 points
   A chain of length 1.2 m and mass per unit length of 0.01 kg is hanging between the tips of two vertical posts separated by a distance of 0.75 m. The left post is 1 m tall while the right post is 0.75 m tall. Considering the effect of gravity, find the chape of the chain in its static equilibrium position. Write a general program to solve the discretized version of this problem as a finite-variable optimization problem. Run your program for different number of discretizations and see how it converges to a continuous shape. Submit your calculations, program, and the plots of the results.