Consider a two-objective optimization problem in which we want to maximize f1(x) and minimize f2(x). Suppose the problem has a square criterion/objective space withy1 [0,1] andy2 [0,1], i.e.y1takes any value from 0 to 1 andy2takes any value from 0 to 1. Which point(s) is (are) Pareto-optimal?

A. (0,0)

B. (1,0)

C. (1,1)

D. (0,0), (1,0) and (1,1)

Which of the following statements about outer linearization is correct?

A. In the Frank-Wolfe algorithm, we determine a sequence of points (x0, x1, x2,... , xn, ...) that gradually approaches the true optimal solution x*. That means, the distance between x_n+1and x* is shorter than that between xnand x*, for all n.

B. Outer linearization tends to overestimate the optimal value of a convex function. That is, if the true optimal value of the function is y*, the estimated optimal value through outer linearization is (y*+ a), where a is a nonnegative constant.

C. Suppose a convex function is inner linearized and outer linearized, and the estimated optimal value is y_inand y_outrespectively. Then we must have y_in>= y_out

D. All of the above statements are correct.