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In a minimization problem, i.e., $\min f(\mathbf{x})$, the procedure is

  1. Start with an arbitrary $\mathbf{x}_1$.
  2. At $i$-th iteration, calculate a gradient $\nabla f(\mathbf{x}_i)$.
  3. Find the next point, $\mathbf{x}_{i+1}\in \mathbf{x}_i+\gamma \nabla f(\mathbf{x}_i)$, where $\gamma$ is a real value that minimizes $f(\mathbf{x}_i+\gamma \nabla f(\mathbf{x}_i))$.

I think both "Frank–Wolfe algorithm" and "Gradient steepest descent algorithm" are the same as the above. What is different?

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    $\begingroup$ The Frank-Wolfe algorithm solves a constrained minimization problem, but your algorithm doesn't, so they're not the same. What description of the Frank-Wolfe algorithm are you basing your assumption on? $\endgroup$ Commented Jun 14, 2018 at 2:05

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The main difference between the two is that steepest desc also contains an scaling operation that depends on the dual norm of the gradient.

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    $\begingroup$ As it’s currently written, your answer is unclear. Please edit to add additional details that will help others understand how this addresses the question asked. You can find more information on how to write good answers in the help center. $\endgroup$
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    Commented Feb 16, 2022 at 19:00

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