Optimizing Across Noisy Domain

[tangodirt]

Are there any established methods for optimizing across a 2D surface with noise? I am trying to find the maximum across a 2D surface, but the surface is extremely noisy. Ideally, I would numerically optimize a function without resorting to computing the entire surface, filtering the surface, and searching for a maximum, but I am not finding any established methods for this.

Any ideas?

 

[Svein]

One effective filtering technique is the median filter (https://en.wikipedia.org/wiki/Median_filter).

 

[jasonRF]

'Optimize' can mean almost anything. The right thing to do will strongly depend on

1. The criterion by which you are defining optimality ,

2. The form of the expression you are optimizing, and

3. Any other detauls that matter: constraints, continuous or discrete space, whether this is somethig that must be solved many time very quickly or if it just done once in awhile and can run a long time to converge, etc.

Unless you provide more details folks here cannot do much to help you.

Jason

 

[tangodirt]

'Optimize' can mean almost anything. The right thing to do will strongly depend on

1. The criterion by which you are defining optimality ,

2. The form of the expression you are optimizing, and

3. Any other detauls that matter: constraints, continuous or discrete space, whether this is somethig that must be solved many time very quickly or if it just done once in awhile and can run a long time to converge, etc.

Unless you provide more details folks here cannot do much to help you.

Jason

1. Maximize/minimize over a known domain.

2. It is a generic function. A black box with two inputs that returns an output that is noisy.

3. Something that needs to be solved many times, very quickly.

Think of this as Excel's "Solver", but with a noisy function.

 

[jasonRF]

I've never used excel's solver - you aren't describing what 'optimal' means. If your function is noisy, the maximum or minimum will likely be due to noise, not what you care about. So ... what does 'optimal' mean in this instance? What do you know about the problem (characteristics of noise, etc.)?

jason

 

[rs1n]

Would the SVD be helpful? It would presumably still require you to compute the entire surface, though.