Comments:

• 1.3) g maps to an m-dimensional vector space. Many were using Hessian notation without explaining what it meant. The first derivative is the Jacobian, a MATRIX of gradients of each g_i.
• 1.5) There was a typo. The function is over two variables, not one. If you assumed it was just a function of x, that is fine.
• 2.1) You have to prove: "Bounded below implies a global minimizer" here, you can't assume it. This is not even true for general convex functions, consider f(x) = e^x.
• 3.1) Was done very well.
• 3.2) This was a tricky question. The trick for part (b) is to form a new quadratic function whose Hessian is the PSD matrix in the question. (The "are the converses true" part was not marked as many overlooked it. Please consider this a recommended exercise.)
• 3.5) Was done well.
• 4.1) You didn't need to have working code to get marks. The point was to get your hands dirty using Matlab. An important thing to note is that Steepest Descent performs very slowly. This is because of the "shape" of the function, which is like a hollowed banana.