  In this paper we consider a problem, called convex projection, of projecting
a convex set onto a subspace. We will show that to a convex projection one can
assign a particular multi-objective convex optimization problem, such that the
solution to that problem also solves the convex projection (and vice versa),
which is analogous to the result in the polyhedral convex case considered in
arXiv:1507.00228. In practice, however, one can only compute approximate
solutions in the (bounded or self-bounded) convex case, which solve the problem
up to a given error tolerance. We will show that for approximate solutions a
similar connection can be proven, but the tolerance level needs to be adjusted.
That is, an approximate solution of the convex projection solves the
multi-objective problem only with an increased error. Similarly, an approximate
solution of the multi-objective problem solves the convex projection with an
increased error. In both cases the tolerance is increased proportionally to a
multiplier. These multipliers are deduced and shown to be sharp. These results
allow to compute approximate solutions to a convex projection problem by
computing approximate solutions to the corresponding multi-objective convex
optimization problem, for which algorithms exist in the bounded case.
  For completeness, we will also investigate the potential generalization of
the following result to the convex case. In arXiv:1507.00228, it has been shown
for the polyhedral case, how to construct a polyhedral projection associated to
any given vector linear program and how to relate their solutions. This in turn
yields an equivalence between polyhedral projection, multi-objective linear
programming and vector linear programming. We will show that only some parts of
this result can be generalized to the convex case, and discuss the limitations.
