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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 followingenter image description here (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!

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 followingenter image description here (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?

any ideas or references would be really welcome.

Thank you!

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 followingenter image description here (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!

Source Link
JumpJump
JumpJump
  • 679
  • 3
  • 13

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 followingenter image description here (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?

any ideas or references would be really welcome.

Thank you!