[SOLVED] ECE509 Homework2-LP problem

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

• min “Ax − b“1 s.t. “x“∞ ≤ 1
• min “x“1 s.t. “Ax − b“∞ ≤ 1
• min “Ax − b“1 + “x“∞

2. Consider the L4-norm approximation problem:

min

where A ∈R^m×ⁿ 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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