algorithm for finding the minimizer of a almost convex function Let $f(t)$ be a function from $(0,1)$ to $\mathbb R$. If $f$ is strictly convex, then finding the minimizer is an easy task. For example, newton's method would be able to do the job.
However, if my function is not convex, but more like the following (please forgive my poor drawing skill...)
That is， the function is "almost" convex but with small perturbation. Then, is there an efficient algorithm which can find an "good enough" minimizer?
PS: the existence of minimizer of $f(t)$ is assumed. 
any ideas or references would be really welcome.
Thank you!
 A: How abou trying to apply the Golden Search algorithm?
A: You could try stochastic optimization methods. The rough idea  is to leverage noise to efficiently explore the landscape of $f(t)$. To quote from the linked article, the injected randomness may enable the method to escape a local optimum and eventually to approach a global optimum.
To illustrate this point, suppose you knew that the only point where $f'(t)=0$ is at the minimizer, then you could use a numerical solution to the SDE:
$$
d Y = - f'(Y) dt + f'(Y) dW
$$ to find the minimizer.  Here $W$ is a standard Brownian motion. Note that this SDE has a fixed point at the minimizer, and away from the minimizer it efficiently explores $f(t)$.    
As a concrete test, consider $f(x) = 1/2 (x-1/2)^2 + \epsilon \cos(10 x \pi)$, which has a global minimum at $x=1/2$ as shown in the figure below with $\epsilon=0.01$.  Starting from the initial condition $0.92$ the method described above converges like a charm to the minimum at $0.5$ in just $32$ steps despite the fact that $f(t)$ is a bit bumpy.

The dots in this figure represent the points along a numerical solution of the SDE by the simple Euler-Maruyama scheme.
A: If you are interested in complexity results, I advice you to look at this paper https://arxiv.org/abs/1501.07242 by Belloni, Liang, Narayanan and Rakhlin. I think their results are nearly optimal when the required accuracy $\epsilon\to 0$; however, their analysis might be overly complicated for your case, as it is suited for higher dimensional settings. 
