10 Matching Annotations
  1. Apr 2018
    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

  2. Jul 2016
    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.