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Suppose that I want to optimize a unimodal function defined on some real interval. I can use the well-known algorithm as described in Wikipedia under the name of ternary search.

In case of the algorithm that repeatedly halving intervals, it is common to reserve the term binary search for discrete problems and to use the term bisection method otherwise. Extrapolating this convention, I suspect that the term trisection method might apply to the algorithm that solves my problem.

My question is whether it is common among academics, and is safe to use in, e.g., senior theses, to apply the term ternary search even if the algorithm is applied to a continuous problem. I need a reputable source for this. I'm also interested whether the term trisection method actually exists.

Pteromys
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Check out Fibonacci search and golden section search (the article about Fibonacci search talks about an array, but the technique is really applicable just like golden section search to continuous functions). Fibonacci search is a tiny bit faster. The trick is that you can reuse the points from one iteration to the next. For Fibonacci, you'll have to determine the number of iterations beforehand. No big deal, you know the precision sought anyway.

It can be shown that if you just compare the function values for relative order, Fibonacci search is fastest possible. If you consider the actual values, some form of quasi-Newton is faster.

vonbrand
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The word "bitonic search" can probably refer to this concept. See this book and these lecture notes for instance.

Hoda
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