10 Matching Annotations
1. Apr 2018
2. wiki.c2.com wiki.c2.com
1. ConvexHull

In mathematics, the convex hull or convex envelope of a set X of points in the Euclidean plane or in a Euclidean space (or, more generally, in an affine space over the reals) is the smallest convex set that contains X. For instance, when X is a bounded subset of the plane, the convex hull may be visualized as the shape enclosed by a rubber band stretched around X. -Wikipedia

URL

3. Jul 2016
4. arxiv.org arxiv.org
1. Ax=b

Apparently $$Ax = b$$ is not required, but is used as a technical prop in subsequent proof construction.

If no linear constraints are found, either A, b can be viewed as zero, or can be viewed as the smallest affine set that includes S. In both cases, this effectively makes the constraint trivial.

2. A

How does one go about choosing (a good) A, especially since it seems to not be necessary to have a non-trivial (A,b) pair?

3. x()=2Feas, that is,1(x)< , establishing the claim

So it appears that we don't need to get feasible points at each iteration?

Answer: correct, this is pointed out later in a couple of pages, where it is stated $$x$$ need not be feasible, but $$x'$$ will be.

4. int(dom(f))

Why isn't $$x \in dom(f)$$ sufficient?

Ah, I think it is sufficient for $$t' = f(x')$$, but we also need $$x \in int(dom(f))$$ for the subsequently mentioned subdifferentials.

5. (x0;t0)2bdy(dom(f))

Confirmed that this should be $$bdy(epi(f))$$, not $$bdy(dom(f))$$

6. because(x;t) =1(x)

Why?

7. a value we now know to be positive and nite

Where is the proof that if $$\alpha_1 (x)$$ is infinite, then $$\alpha_2 (x,t)$$ is finite?

I now see that it starts at the beginning of page 3, but without any forward reference it seems that it is being skipped.

8. Approximating2(x;t) is the same as approximating the solutionto() = 0,

Not completely clear to me why this is the case.

9. Assume eis a known feasible point contained in int(S\dom(f)).

How to pick? Perhaps a reference to strategies, or note that strategies will be discussed later.