Frank–Wolfe algorithm: Difference between revisions

Revision as of 22:23, 23 October 2013

Revision as of 22:23, 23 October 2013

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</math>

The latter optimization problem is solved in every iteration of the Frank-Wolfe algorithm, therefore the solution <math>\mathbf{s}_k</math> of the direction-finding subproblem of the <math>k</math>-th iteration can be used to determine increasing lower bounds <math>u_kl_k</math> during each iteration by setting <math>u_0l_0 = - \infty</math> and

:<math>

u_kl_k := \max (u_l_{k - 1}, f(\mathbf{x}_k) + (\mathbf{s}_k - \mathbf{x}_k)^T \nabla f(\mathbf{x}_k))

</math>