1. (containing (a)-(d)) Consider the problem (P) min ry subject to sty 2 2, ry. (1) (a) State FONC and 50NC for the following constrained optimization problem: min /(x) subject to r e n. () (b) Find all points satisfying the FONC for problem (P). Hint: you need to consider all the interior points and boundary points. The tangent directions for the graph of y = g(x) at (x, y] is parallel to [1, s'(x)]], and the normal direction is parallel to [o'(x), -1]". You can use this to compute feasible directions on the boundary of the constraint set. Or you can also use the graphs to compute the directions. You don't need to prove that the directions you obtained are feasible directions. (c) Which of the point(s) in part (b) satisfy the SONC? Explain your solution. (d) Which of the point(s) in part (b) are local minimizers? Explain your solution