shrink (0) = 0

Given a point xo ER, the shrink function is defined as the unique solution to the following optimization problem: shrink(xo) = arg min |x| +5(x xo)2. XER 2.4: (i) Assuming xo > 0, find all points (y, u) satisfying the KKT conditions for the problem min y2 +5(y1 xo) such that y2 > y1, y2 > -41. Y1,2 HINT: It is helpful to split into the 3 cases {f1 > 0,42 >0}, {u1 > 0, M2 = 0}, and {M1 = 0, M2 >0}. (ii) Using your previous work compute shrink(1/2) and shrink(4). Given a point xo ER, the shrink function is defined as the unique solution to the following optimization problem: shrink(xo) = arg min |x| +5(x xo)2. XER 2.4: (i) Assuming xo > 0, find all points (y, u) satisfying the KKT conditions for the problem min y2 +5(y1 xo) such that y2 > y1, y2 > -41. Y1,2 HINT: It is helpful to split into the 3 cases {f1 > 0,42 >0}, {u1 > 0, M2 = 0}, and {M1 = 0, M2 >0}. (ii) Using your previous work compute shrink(1/2) and shrink(4)