Which of the following methods is a local optimization approach?

Question

BlackTom AI · Accepted Answer

Question: Which of the following methods is a local optimization approach?

Given data shows only one provided option and no list of answer choices beyond it. We will reason about the supplied option and discuss the local optimization concept in general, while noting the absence of other alternatives.

Option provided: "Perform a linear search on the input and use it to evaluate the function along a chosen search direction."

Analysis:
- This statement describes evaluating the objective function along a specific direction and using those evaluations to guide progress. In optimization terminology, evaluating the function along a direction and selecting an appropriate step is characteristic of a line search strategy, which is commonly embedded within local optimization methods such as gradient descent or quasi-Newton methods. Line search aims to find an acceptable step size that sufficiently reduces the objective locally, without attempting to explore the entire domain globally. Therefore, the method aligns with local optimization techniques that rely on local information (current point and a direction).
- The phrase "linear search on the input" could be interpreted as probing along a line in the search space. In many local methods, the search is performed along a chosen direction (often derived from gradient, current approximation, or previous steps) and a line search is used to determine the step length. This reinforces that the described approach fits the category of local optimization.

What makes this plausible as a local optimization approach:
- It uses information available at the current iterate (the chosen search direction) rather than evaluating the objective across the entire domain or multiple distant regions.
- The process seeks a better (lower) objective value in a neighborhood of the current point, which is the essence of local optimization.

Why this might be considered incorrect if other options existed:
- If there were choices that described global optimization techniques (e.g., exhaustive search, random global sampling, multi-start strategies that explore far from the current region), those would not be local optimization methods.
- If there were options specifying purely derivative-free global heuristics without local convergence guarantees, they might not qualify as local optimization depending on context.

Summary of reasoning given the available information:
- The described approach (searching along a chosen direction and evaluating the function to guide progress) is consistent with local optimization practices such as line search within a local method. Without the rest of the option set, we cannot contrast it with other alternatives, but the approach itself is a recognized local optimization technique.

25S-STATS-102B-LEC-3 Quiz 2- Requires Respondus LockDown Browser

Which of the following methods is a local optimization approach?

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