Frank–Wolfe algorithm: Difference between revisions

Revision as of 02:30, 20 August 2013

Revision as of 19:53, 12 October 2013

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:Interpretation: Minimize the linear approximation of the problem given by the first-order [[Taylor series|Taylor approximation]] of f around <math>\mathbf{x}_k \!</math>.

:'''Step 2.''' Step size determination. Set <math>\gamma \leftarrow \frac{2}{k+2}</math>, or alternatively find <math>\gamma \!</math> that minimizes <math> f(\mathbf{x}_k+\gamma(\mathbf{s}-\mathbf{x}_k))</math> subject to <math>0 \le \gamma \le 1</math> .

:'''Step 3.''' Update. Let <math>\mathbf{x}_{k+1}\leftarrow \mathbf{x}_k+\gamma(\mathbf{s}-\mathbf{x}_k)</math>, let <math>k \leftarrow k+1</math> and go back to Step 1.