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The fact that there is only a single, global optimum, σ*, for each case is a consequence of P v being a unimodal function in σ.
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Thus, the function p(α n ) is a unimodal function.
It is adapted to solve (3.2) when the object function is a unimodal function.
It is a unimodal function of the coupling coefficient and the quality factor.
However, in all of our numerical simulations, we have always noted that the function p(α n ) is a unimodal function.
We find that the system cost of an IHP is a unimodal function of the station service area size and can be efficiently solved in a sub-linear time by the bisection algorithm.
The function p(α n ), p ( α n ) = p ~ ( α n ) + ρ 2 ( α n - θ ) 2, (60). is a unimodal function on the interval α n ∈ [ 0, α n max ] for the condition C. Proof: 1.
First, in Lemma 1, we show that the function p(α n ) is a unimodal function on the interval α n ∈ [ 0, α n max ] for the condition: C) θ ≤ ϕ.
Based on this observation, in Appendix 1, we have provided the condition for which p(α n ) is a unimodal function and propose the bracketing method[30, 31] to solve problem (44).
Martin and Gaddy function is a unimodal function.
Because sphere's function is a unimodal function, we could not use it for search multi-minima.
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