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Basically, I have an S-shape quasiconvex function which becomes a straight line at its end points. Can bisection algorithm handle these points to find an optimum? $f(t)=a e^{-b e^{-c (t-d)}}$ If yes how can I show these sublevel sets as convex inequalities?(couldn't find anything relevant in Boyd's book)

Thanks in advance.

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    What do you consider optimal? Isn't $t \to \infty$ optimal? (or $-\infty$ depending on the sign of $a$, $b$, $c$). – 2017-01-17
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    thanks for answering. All the coefficients are positive and the domain is bounded and the function is nondecreasing in its domain. I set them as $a=0.2, b=1, c=8, d=6.25$ – 2017-01-17
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    Then, depending on whether you want to minimize or maximize, you pick the left or the right endpoint of the domain as the optimal solution, right? – 2017-01-17
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    yes exactly but at the end or beginning of function it become almost a line. – 2017-01-17
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    so why do you need a bisection algorithm? – 2017-01-17
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    well, this is my objective function in a quasiconvex optimization problem. Since quasiconvex functions have local minima(in my case at its end points) I guess I have to use bisection method. Here is my objective function:$ Minimize \quad\sum_{h=1}^H\sum_{i=1}^{I}(\sum_{p \in \mathcal P_{i}}t_{i,p}^h)f(\sum_{p \in \mathcal P_{i}}t_{i,p}^h) $ I also ask another question regarding to its sublevel sets http://math.stackexchange.com/questions/2044939/how-to-show-sublevel-sets-of-a-quasiconvex-function-as-its-convex-inequalities – 2017-01-17
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    Maybe post your full problem instead of riddles. – 2017-01-17

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