Are there other ways to deal with problems that don't have optimization solutions?
keenan
@rbunny Great question. Yes, sometimes the way we want to specify a problem is not compatible with the way a numerical solver "thinks" about problems. For instance, we might have a bunch of disjoint constraints we want to satisfy simultaneously---and are willing to tolerate a solution that satisfies these constraints "as well as possible."
In the graphics/geometry context, there's an algorithm called ShapeUp that takes this approach. The paper gives a nice explanation (with good pictures) of how you can get this "near satisfaction" of constraints by alternating projection onto the individual constraint sets. There are other similar techniques, which often come under the heading of "infeasible" methods.
Are there other ways to deal with problems that don't have optimization solutions?
@rbunny Great question. Yes, sometimes the way we want to specify a problem is not compatible with the way a numerical solver "thinks" about problems. For instance, we might have a bunch of disjoint constraints we want to satisfy simultaneously---and are willing to tolerate a solution that satisfies these constraints "as well as possible."
In the graphics/geometry context, there's an algorithm called ShapeUp that takes this approach. The paper gives a nice explanation (with good pictures) of how you can get this "near satisfaction" of constraints by alternating projection onto the individual constraint sets. There are other similar techniques, which often come under the heading of "infeasible" methods.