Optimization Method
Updated 2026-08-10
INTRODUCTION
English translation pending.
CORE DEFINITION
A family of mathematical search methods, including golden-section search and Fibonacci search, that locate an optimum with the fewest possible trials. Its proposition is that when exhaustive enumeration is impossible, a structured strategy that exploits the shape of the response surface is far more efficient than random testing. Qualifier: the methods assume a unimodal or ordered response, so multi-peaked functions require different techniques.
SCAFFOLDING EFFECT
Reduce cognitive load
- Smart trial: Replace random testing with a search strategy that gains information from each attempt. - Interval reduction: Discard the weaker portion of the range each round to shrink the search space fast. - Efficient search: Locate an optimum with far fewer experiments than exhaustive or random approaches.
Anchor fast decisions
When the response is unimodal, comparing two interior points tells you which side of the interval can be discarded. Golden-section and Fibonacci search place those points at fixed ratios, so each new trial eliminates a predictable fraction of the remaining range. Repeating the step converges on the optimum geometrically, which is why it beats scanning or guessing.
MINIMUM ACTION
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