  In this work, we consider a class of convex optimization problems in a real
Hilbert space that can be solved by performing a single projection, i.e., by
projecting an infeasible point onto the feasible set. Our results improve those
established for the linear programming setting in Nurminski (2015) by
considering problems that: (i) may have multiple solutions, (ii) do not satisfy
strict complementary conditions, and (iii) possess non-linear convex
constraints. As a by-product of our analysis, we provide a quantitative
estimate on the required distance between the infeasible point and the feasible
set in order for its projection to be a solution of the problem. Our analysis
relies on a "sharpness" property of the constraint set; a new property we
introduce here.
