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Step 3. Direction-finding subproblem. Solve for <math>\bar{x_k}</math>
:Minimize <math>\nabla^T f(x_k) \bar{x_k}</math>
:Subject
(note that this is a Linear Program. <math>x_k</math> is fixed during Step 3, while the minimization takes place by varying <math>\bar{x_k}</math>).
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