Which of the following is NOT true about the steepest descent method?

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BlackTom AI · Accepted Answer

Question restatement: Which of the following is NOT true about the steepest descent method?

Option 1: 'It is highly dependent on the initial guess' In steepest descent, the starting point can significantly influence the convergence path and potentially lead to different local minima or convergence rates, so this statement is consistent with how the method behaves.

Option 2: 'The size of the step may change at every iteration' In practice, step sizes are often adapted, either by a line search or a predetermined schedule, to improve convergence and stability, making this statement true.

Option 3: 'There is no need to compute any derivative' Steepest descent fundamentally relies on gradients (derivatives) to identify the descent direction. Computing a derivative is essential to determine the direction of steepest descent, so claiming no derivatives are needed is incorrect.

Option 4: 'The gradient needs to be computed at every iteration' This is a core requirement of the method: at each iteration, the gradient (or an equivalent directional derivative) is evaluated to guide the next step, so this statement is true.

Rationale across options: The steepest descent algorithm uses the gradient to move toward lower objective values, so derivative information is central. The initial point and step-size strategy influence convergence behavior, but derivative absence would fundamentally undermine the algorithm’s purpose. Examining each choice shows that the statement claiming no derivatives are needed stands in direct conflict with the method’s core mechanism, while the remaining statements align with standard descriptions of how steepest descent operates.

Which of the following is NOT true about the steepest descent method?Single choice

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