Lesson plan
Interior-point method
Interior-point methods (also referred to as barrier methods or IPMs) are algorithms for solving linear and non-linear convex optimization problems. IPMs combine two advantages of previously-known algorithms: * Theoretically, their run-time is polynomial—in contrast to the simplex method, which has exponential run-time in the worst case. * Practically, they run as fast as the simplex method—in contrast to the ellipsoid method, which has polynomial run-time in theory but is very slow in practice. In contrast to active-set methods (such as the simplex method) which traverses the boundary of the feasible region, and the ellipsoid method which bounds the feasible region from outside, an IPM reaches a best solution by traversing the interior of the feasible region—hence the name.
Article summary
Interior-point methods (also referred to as barrier methods or IPMs) are algorithms for solving linear and non-linear convex optimization problems. IPMs combine two advantages of previously-known algorithms: * Theoretically, their run-time is polynomial—in contrast to the simplex method, which has exponential run-time in the worst case. * Practically, they run as fast as the simplex method—in contrast to the ellipsoid method, which has polynomial run-time in theory but is very slow in practice. In contrast to active-set methods (such as the simplex method) which traverses the boundary of the feasible region, and the ellipsoid method which bounds the feasible region from outside, an IPM reaches a best solution by traversing the interior of the feasible region—hence the name.
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Discussion questions
- Summarise the article in your own words. Which single claim would you verify first, and why?
- Which claim in this article is most likely to be revised as the sources update? How would you check its current status?
- If two sources disagreed about one of these facts, what would you need in order to trust one over the other?
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