Consider problem min XER, y, zER S.t. cTx xx yz y 20 z 0....

Transcribed Image Text:

Consider problem min XER", y, zER S.t. cTx x¹x ≤ yz y 20 z ≥ 0. min XER", y,ZER S.t. Note that the function h(x, y, z) := x¹x - yz is not a convex function, so the above problem is not convex. However, it can be reformulated as a convex SOC optimization problem. Prove that the constraint (2b) and the SOC constraint (3b) below are equivalent. cTx 2x |(²x)|* y≥0 z ≥ 0. (2a) (2b) (2c) (2d) ≤y+z (3a) (3b) (3c) (3d) Consider problem min XER", y, zER S.t. cTx x¹x ≤ yz y 20 z ≥ 0. min XER", y,ZER S.t. Note that the function h(x, y, z) := x¹x - yz is not a convex function, so the above problem is not convex. However, it can be reformulated as a convex SOC optimization problem. Prove that the constraint (2b) and the SOC constraint (3b) below are equivalent. cTx 2x |(²x)|* y≥0 z ≥ 0. (2a) (2b) (2c) (2d) ≤y+z (3a) (3b) (3c) (3d)