Assignment:
Q1. Which of the following statements are true for f(x) = x2?
a. f(x) is a concave function
b. f(x) c. f(x) >/= 5 is a convex set
d. none of the above
Q2. Which of the following statements are true for f(x) = 3x2 + 2x + 5?
a. f(x) is not a concave function
b. f(x) c. f(x) > /= 2 is a convex set
d. all of the above
Q3. Which of the following statements are true for an unconstrained optimization problem?
a. At a global min or max all partial derivatives will be equal to 0.
b. The first-order optimally conditions are used to find the local maxima and local minima.
c. At a local min or max all partial derivatives will be equal to 1.
d. none of the above
Q4. The Lagrange multiplier _______________.
a. is the shadow price
b. in not valid over a range of changes in the RHS
c. is the rate of change in the objective value as the RHS of the constraint increases
d. all the above
Q5. The optimal value function of a portfolio analysis problem solved using quadratic programming is __________________.
a. called the efficient frontier
b. hurt when an active constraint is tightened
c. a piecewise quadratic convex function
d. all the above
Q6. Increasing the RHS on a nonlinear
a. can contract the constraint set
b. may contract the constraint set
c. may hurt the optimal objective value
d. none of the above