I read on Quora someone posting an image about how the graphical method works, in Simplex. My question is simple:
Why is the sequence vertex A - B - C? I'm pretty sure it should skip directly from A to C, since this algorithm, while being at A, would evaluate all adjacent vertex, to find the best one, so from A, the next one has to be C. Is this correct?
Here's the image:
The problem here is that it may be hard to tell that C is better than B. Depending on the strategy (largest improvement, longest step length, anti-cycling), the "wrong" vertex can be selected. In fact, that's common. The simplex method almost never takes the shortest path to the optimal vertex. A good example is Klee–Minty cube.