Consider the following semi-definite programming problem (P) Minimizexes trace(CX) Subject to X=1, i=1,2,3, X 0,...

 

Transcribed Image Text:

Consider the following semi-definite programming problem (P) Minimizexes trace(CX) Subject to X=1, i=1,2,3, X \ 0, where S3 is the set of all symmetric (3 3) matrices, X0 means X is a positive semi-definite matrix and 3 20 C = 2 30 001 i) Find the optimal value of (P) and an optimal solution for (P). ii) Formulate the dual problem of problem (P). iii) Find the optimal value of the dual problem in part ii). Provide clear reasons for your answer. [Note: You do NOT need to solve the dual problem] Consider the following semi-definite programming problem (P) Minimizexes trace(CX) Subject to X=1, i=1,2,3, X \ 0, where S3 is the set of all symmetric (3 3) matrices, X0 means X is a positive semi-definite matrix and 3 20 C = 2 30 001 i) Find the optimal value of (P) and an optimal solution for (P). ii) Formulate the dual problem of problem (P). iii) Find the optimal value of the dual problem in part ii). Provide clear reasons for your answer. [Note: You do NOT need to solve the dual problem]