Optimization: Difference between revisions

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The Manhattan norm or taxicab norm aka ''L''1 norm resembles movement of taxicabs in Manhattan – it can only traverse horizontally or vertically. A diagonal movement mounts to two steps.

The Chebyshevian norm aka ''L''infinity norm is the opposite of the ~~Minkowskian~~ norm – it is the maximum number of steps in any direction, so a diagonal movement is the same as a horizontal or vertical one.

The Chebyshevian norm aka ''L''infinity norm is the opposite of the Manhattan norm – it is the maximum number of steps in any direction, so a diagonal movement is the same as a horizontal or vertical one.

It should be noted that the dual norm of ''L''1 is ''L''infinity, and vice versa. Thus, the ~~Minkowskian~~ norm corresponds to the ''L''infinity tuning space, and the Chebyshevian norm corresponds to the ''L''1 tuning space. The dual of ''L''2 norm is itself, so the Euclidean norm corresponds to Euclidean tuning as one may expect.

It should be noted that the dual norm of ''L''1 is ''L''infinity, and vice versa. Thus, the Manhattan norm corresponds to the ''L''infinity tuning space, and the Chebyshevian norm corresponds to the ''L''1 tuning space. The dual of ''L''2 norm is itself, so the Euclidean norm corresponds to Euclidean tuning as one may expect.

== Enforcement ==

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 The Manhattan norm or taxicab norm aka ''L''<sup>1</sup> norm resembles movement of taxicabs in Manhattan – it can only traverse horizontally or vertically. A diagonal movement mounts to two steps.
-The Chebyshevian norm aka ''L''<sup>infinity</sup> norm is the opposite of the Minkowskian norm – it is the maximum number of steps in any direction, so a diagonal movement is the same as a horizontal or vertical one.
+The Chebyshevian norm aka ''L''<sup>infinity</sup> norm is the opposite of the Manhattan norm – it is the maximum number of steps in any direction, so a diagonal movement is the same as a horizontal or vertical one.
-It should be noted that the dual norm of ''L''<sup>1</sup> is ''L''<sup>infinity</sup>, and vice versa. Thus, the Minkowskian norm corresponds to the ''L''<sup>infinity</sup> tuning space, and the Chebyshevian norm corresponds to the ''L''<sup>1</sup> tuning space. The dual of ''L''<sup>2</sup> norm is itself, so the Euclidean norm corresponds to Euclidean tuning as one may expect.
+It should be noted that the dual norm of ''L''<sup>1</sup> is ''L''<sup>infinity</sup>, and vice versa. Thus, the Manhattan norm corresponds to the ''L''<sup>infinity</sup> tuning space, and the Chebyshevian norm corresponds to the ''L''<sup>1</sup> tuning space. The dual of ''L''<sup>2</sup> norm is itself, so the Euclidean norm corresponds to Euclidean tuning as one may expect.
 == Enforcement ==