2 Problems (Pri) equivalences Recall the three (simplied) equivalent problems presented in the slides. Here we ignore the linear constraints Ax = b. We assume that the data H >- 0, 'F 0; and that the feasible set is nonempty. We also assume that the parameters are given, xed. Note that it makes sense to assume the positivity, i.e., that the desired return 1",, > 0, and the acceptable risk or; > 0. st. 3T3: 1 [Prl] fTa: = 1",, max chc s.t. 8T3: = 1 [Pr2) min tha: + %ccTH:c s.t. 3T3: = 1 (Pr3) Let pi,p,p be the optimal values, respectively. Let mi,:c,:c be the optimal solutions, respectively. 2.1 Finite optimal values Using the properties of the problems and the data, show that all three optimal values are nite. 2.2 Attainment Show that all three optimal values are attained and provide appropriate equations for nding them