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Convex Optimization by Lieven Vandenberghe, Stephen Boyd

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Chapter 8

Geometric problems

8.1  Projection on a set

The distance of a point x0 Rn to a closed set C Rn, in the norm · , is defined as

The infimum here is always achieved. We refer to any point z C which is closest to x0, i.e., satisfies z x0 = dist(x0, C), as a projection of x0 on C. In general there can be more than one projection ...

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