Frank–Wolfe algorithm: Difference between revisions

Revision as of 10:37, 15 January 2007

Revision as of 10:39, 15 January 2007

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Step 3. Direction-finding subproblem. Solve for <math>\bar{x_k}</math>

:MaximizeMinimize <math>\nabla^T f(x_k) \bar{x_k}</math>

:Subject to <math>\bar{x_k} \epsilon \mathbf{P}</math>

(note that this is a Linear Program. <math>x_k</math> is fixed during Step 3, while the maximizationminimization takes place by varying <math>\bar{x_k}</math>).

Step 4. Step size determination. Find <math>\lambda</math> that minimizes <math> f(x_k+\lambda(\bar{x_k}-x_k))</math> subject to <math>0 \le \lambda \le 1</math> . If <math>\lambda = 0</math> then Stop, we have found the minimum.