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Simple Unconstrained Optimization Method

This Demonstration shows the simple one-dimensional unconstrained maximization algorithm for finding the (local) maximum of the function near the starting value . It is a nongradient method and it requires only the starting value and the initial step value .

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Assume that the function has a single local maximum on the interval . For the given real numbers and , construct the sequences and in the following way:
.
It can be proved that the sequence converges to . The method is simple and easy to implement. It does not require the differentiability of the function nor any additional condition on and . This method is also known as simplex method I and has a linear convergence.
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