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I am coming across a project that involves with "manifold optimization". I don't know what that is. After Googling for a bit, my understanding is that we use a low dimensional surface to approximate the high dimensional objective function (utilizing the structure of the obj func). Then, we carry on our favourite optimization techniques on this low diemsnional surface.

My friend told me this is incorrect. Can someone please explain to me what exactly is manifold optimization in human understandable lanaguage?

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