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for example, a solid cube is convex; however, anything that is hollow or dented, for example, a crescent shape, is non-convex.
Ωστόσο, κάτι που είναι κοίλο ή χτυπημένο, για παράδειγμα, ένα ημισελήνο σχήμα , είναι μη κυρτά.
and also considered the "convex" closure of a problem of non-convex minimization—that is, the problem defined as the closed convex hull of the epigraph of the original problem.
and also considered the "convex" closure of a problem of non-convex minimization—that is, the problem defined as the closed convex hull of the epigraph of the original problem.
comparing the left array and the right pane, one confirms that the right-hand plus-symbol is indeed the sum of the four plus-symbols from the left-hand sets, precisely two points from the original non-convex summand-sets and two points from the convex hulls of the remaining summand-sets.__the shapley–folkman lemma is illustrated by the minkowski addition of four sets.
comparing the left array and the right pane, one confirms that the right-hand plus-symbol is indeed the sum of the four plus-symbols from the left-hand sets, precisely two points from the original non-convex summand-sets and two points from the convex hulls of the remaining summand-sets._: {0, 1} + {0, 1} = {0 + 0, 0 + 1, 1 + 0, 1 + 1} = {0, 1, 2}.