Dykstra's projection algorithm
Dykstra's projection algorithm is like a game where you want to put a picture on a wall, but the wall has some bumps that make it hard to get the picture to sit flat.
First, you take the picture and put it on the wall where you think it should be. But then you notice the bumps. So, you take the picture off the wall and instead put a sheet of plastic on the wall, where you draw the bumps.
Next, you take the picture again and put it on the plastic sheet so that the picture is touching it. Then you take a special tool and push the picture down onto the plastic sheet. This tool helps smooth out the bumps in the wall and make the picture sit flat.
After that, you take the picture off the plastic sheet and look at how it sits on the wall. You might notice that there are still some spots where the picture isn't sitting completely flat, so you repeat the process again with the plastic sheet until the picture sits entirely flat on the wall.
In math terms, Dykstra's algorithm helps us find the closest point to a set of points that satisfies a bunch of conditions (kind of like the picture sitting flat on the wall). It does this by constructing a series of projections onto other sets of points until we get as close as possible.
First, you take the picture and put it on the wall where you think it should be. But then you notice the bumps. So, you take the picture off the wall and instead put a sheet of plastic on the wall, where you draw the bumps.
Next, you take the picture again and put it on the plastic sheet so that the picture is touching it. Then you take a special tool and push the picture down onto the plastic sheet. This tool helps smooth out the bumps in the wall and make the picture sit flat.
After that, you take the picture off the plastic sheet and look at how it sits on the wall. You might notice that there are still some spots where the picture isn't sitting completely flat, so you repeat the process again with the plastic sheet until the picture sits entirely flat on the wall.
In math terms, Dykstra's algorithm helps us find the closest point to a set of points that satisfies a bunch of conditions (kind of like the picture sitting flat on the wall). It does this by constructing a series of projections onto other sets of points until we get as close as possible.