Exam 3

Exercise 3. Consider the following multi-objective problem:

$$\left\lbrace \begin{array}{ll} \mathrm{minimize} & x_2 \ ,-x_1 -2x_2 \\ s\ldotp t & x_1 \ge 0\\ & x_2 \ge 0\\ & x_1 +x_2 \le 5 \end{array}\right.$$

3.1 Is it a convex problem? Why?

3.2 Do minima exist? Why?

3.3 Is the point (0, 2) a weak minimum? Why?

3.4 Find all the minima by using the scalarization method.

3.5 Find all the weak minima by using the scalarization method.

3.6 Find the ideal point.

3.7 Apply the goal method with ${\left|\ldotp \right|}_1$

3.8 Apply the goal method with ${\left|\ldotp \right|}_2$