We would like to minimize the function f : R³  → R, with values:

with the constraint ΙΙxΙΙ_∞ < 1. Explain precisely how to formulate the problem as an SOCP in standard form.

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f(x) = max (x₁+x2 min (min(x₁+2, x2 + 2x₁-5), X3-6), - (x1 − x3)² + 2x²), 1-X1