 Solution

ID: past-exam-of-the-numerical-linear-algebra-and-continuous-optimisation-course-of-the-university-of-oxford/2010/b/6/ii/solution

c_{i} (x) > 0

B_{μ} (x) = f (x) - μ i = 1 \sum m lo g c_{i} (x) .

With

y_{i} (x) = μ / c_{i} (x)

, its gradient is

\nabla B_{μ} (x) = g (x) - A (x)^{T} y (x) .

y_{i}

are the barrier's multiplier estimates.

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