Comments Assignment 3

2.1: This question was not done very well. Students had trouble presenting a proof by contradiction here, and many students only presented the non-strict case, but not the strict case.
2.3: Most students were able to show the function was convex and find the gradient to state necessary and sufficient conditions for optimality, but had trouble finding the solution for the triangle with vertices (0,0), (3,0), and (1,2).
2.5: Fairly well done. Many students assumed that if s is a feasible direction at x, then x+s is feasible, which may not be true.
2.6: Well done, no problems here.
2.7: Most were able to show this cylindrical can problem is equivalent to the constrained convex problem. Different techniques were used to show the new objective function was convex. Those who used the Hessian had trouble showing it was positive semidefinite. Others simply showed e^x was convex, and explained that the objective function was therefore convex. For the last part of the problem, some students did not seem to fully understand that this was a constrained problem and had trouble using Exercise 2.6. Also, some wanted to use the original problem in the last part instead of the convex formulation from the first part.
2.9: Some confusion about showing the new problem was Slater regular rather than the original (CO) problem.

1. Optimality Well done, but some did not explain why the critical point z = (3,0.5) was actually a minimum. Some noticed that f(x) >= 0 for all x and that f(z) = 0 to conclude it was a minimum. Others tried to show the function was convex.
2. Products and Ratios of Convex Functions Students found this to be quite difficult. A few assumed the functions were differentiable in order to do these questions.
3. Constrained Optimization Most students didn't seem to be able to handle constrained optimization very well. Some completely disregarded the constraints altogether. more details to come ?????