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Figure 4
Comparison of iterative updates between the gradient descent method and the subgradient projection for several cases. (a) An example using the gradient descent method. (b)–(d) Examples using the iterative subgradient projection. (b) shows the case where the minimum value of the objective function g is 0, and (c) and (d) show the case where the minimum value is E. In (c) and (d), the constants used in the subgradient projection are 0 and ξ, respectively. The three-dimensional schematic diagram in the upper panels is projected to a two-dimensional plane and is shown in the lower panels. The color of the points represents the number of iterations, and the arrows indicate the transition of each update. The plane at g(x) = 0 is shown in light gray and the plane at g(x) = ξ in light blue. In the bottom diagram of (d), the area where g(x) ≤ ξE is shown in blue.

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CRYSTALLOGRAPHY
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