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Our approach, the closest point method for manifold mapping, reduces the problem of solving a constrained PDE between manifolds M and N to the simpler problems of solving a PDE on M and projecting to the closest points on N. In our approach, an embedding PDE is formulated in the embedding space using closest point representations of M and N.
However, the problems of solving strongly convex optimization subproblems and of finding shrinking projections in [15, 16] is expensive excepts special cases when the feasible set has a simple structure.
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