Problem 6. [9%] Consider the optimization problem. Az where A € Rnxd and b ER". Solve the following points. 1. Compute t

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Problem 6 9 Consider The Optimization Problem Az Where A Rnxd And B Er Solve The Following Points 1 Compute T 1 (30.82 KiB) Viewed 72 times

Problem 6. [9%] Consider the optimization problem. Az where A € Rnxd and b ER". Solve the following points. 1. Compute the dual problem (using the Fenchel-Rockafellar duality theory). Hint: put the problem in the form f(x) + 9(Ac) 2. Does strong duality hold? Justify the answer. (Hint: the dual of the dual problem is the primal. So, in order to ensure strong duality one can check the qualification condition on the dual problem. 3. Write the KKT conditions. 4. Derive a rate of convergence on the primal iterates from the application of FISTA on the dual problem. (Hint: recall the it is possible to bound the square of the distance to the primal solution by the dual objective values