Around the internet, I have seen scattered references to the idea of rescaling an objective function and using that as a PDF for the purpose of optimization. (On this site for example: Do optimization techniques map to sampling techniques?) Can someone point me to a place where I can learn more about this method? (Papers, blog posts, lectures, etc.)

The idea, as I've seen it, is to take your objective function $f(x)$ and create a new function $g(x) = e^{kf(x)}$, where $k$ is a very large number for a maximization problem or a very large negative number for a minimization problem. The new function $g(x)$ will then be much higher at the global optimum than anywhere else. If $g(x)$ is then treated as an unnormalized probability density function, most samples drawn from that distribution will be around that optimum.

Things I want to know include, but are not limited to:

1. Which sampling algorithms are effective for these probability functions?
2. Why is this method not used more frequently? (It seems like it could be so effective). In other words, are there arguments against it?
3. Are there any variants of this method that improve efficiency or performance?

Around the internet, I have seen scattered references to the idea of rescaling an objective function and using that as a PDF for the purpose of optimization. (On this site for example: Do optimization techniques map to sampling techniques?) Can someone point me to a place where I can learn more about this method? (Papers, blog posts, lectures, etc.)

The idea, as I've seen it, is to take your objective function $f(x)$ and create a new function $g(x) = e^{kf(x)}$, where $k$ is a very large number for a maximization problem or a very large negative number for a minimization problem. The new function $g(x)$ will then be much higher at the global optimum than anywhere else. If $g(x)$ is then treated as an unnormalized probability density function, most samples drawn from that distribution will be around that optimum.

Things I want to know include, but are not limited to:

1. Which sampling algorithms are effective for these probability functions?
2. Why is this method not used more frequently? (It seems like it could be so effective). In other words, are there arguments against it?
3. Are there any variants of this method that improve efficiency or performance?

Around the internet, I have seen scattered references to the idea of rescaling an objective function and using that as a PDF for the purpose of optimization. (This post, for example) Can someone point me to a place where I can learn more about this method? (Papers, blog posts, lectures, etc.)

The idea as I've seen it is to take your objective function $f(x)$ and create a new function $g(x) = e^{kf(x)}$, where $k$ is a very large number for a maximization problem or a very large negative number for a minimization problem. The new function $g(x)$ will then be much higher at the global optimum than anywhere else. If $g(x)$ is then treated as an unnormalized probability density function, most samples drawn from that distribution will be at that optimum.

Things I want to know include, but are not limited to: What sampling algorithms are effective for these probability functions? Why is this method not used more frequently..it seems like it could be so effective? Are there any variants of this method that improve efficiency or performance?

Around the internet, I have seen scattered references to the idea of rescaling an objective function and using that as a PDF for the purpose of optimization. (On this site for example: Do optimization techniques map to sampling techniques?) Can someone point me to a place where I can learn more about this method? (Papers, blog posts, lectures, etc.)

The idea, as I've seen it, is to take your objective function $f(x)$ and create a new function $g(x) = e^{kf(x)}$, where $k$ is a very large number for a maximization problem or a very large negative number for a minimization problem. The new function $g(x)$ will then be much higher at the global optimum than anywhere else. If $g(x)$ is then treated as an unnormalized probability density function, most samples drawn from that distribution will be around that optimum.

Things I want to know include, but are not limited to:

1. Which sampling algorithms are effective for these probability functions?
2. Why is this method not used more frequently? (It seems like it could be so effective). In other words, are there arguments against it?
3. Are there any variants of this method that improve efficiency or performance?