[Solved] ECE509 Homework2-LP problem

1. Given A R^mn and b R^m, cast each of the following problems as LP

• min Ax b1 s.t. x 1
• min x1 s.t. Ax b 1
• min Ax b1 + x

2. Consider the L4-norm approximation problem:

min

where A R^mn and b R^m. Formulate this problem as a QCQP.

3. Consider the LP problem:

min e^Tx + f

s.

Find A₀, ,A_n to formulate this problem as a SDP:

min e^Tx + f

s.t. A₀ + A₁x₁ + + A_nx_n 0

4. Consider the optimization problem

min f(x) s.t. x 0

where f is convex. Let x be a point such that

Prove that x is a solution of the optimization problem.

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