In the steepest descent method, the direction at every iteration is

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In this question about the steepest descent method, we are asked to identify the direction used at each iteration.
Option 1: 'Parallel to the tangent of the iso-line' is not correct. The tangent direction lies along a level set, where the function value is constant, and the gradient is perpendicular to that tangent, so moving parallel to the tangent does not decrease the objective in general.
Option 2: 'Perpendicular to the tangent of the iso-line' is correct. The steepest descent direction is the negative of the gradient, which is normal to the iso-lines (level curves). This means it points directly across the level set where the function value changes most rapidly, yielding the steepest decrease.
Option 3: 'Randomly chosen' is incorrect. Steepest descent deterministically uses the gradient direction (specifically, the negative gradient) to guarantee the maximal immediate decrease in the objective among all unit directions, not a random choice.
Option 4: 'Tangent to the iso-line' is incorrect for the same reason as option 1; the tangent direction lies along the level set and does not decrease the function value in general, since moving along a level line leaves the function value unchanged.
Thus, the only option that aligns with the mathematical principle of steepest descent is the perpendicular-to-tangent choice.

BN5206 Week 5 online quiz

In the steepest descent method, the direction at every iteration is

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