Is the normal cone of a polyhedron a set of points or a set of vectors?

by jaja   Last Updated May 06, 2018 02:20 AM

I looked for the normal cone to a polyhedron, and I found this definition from https://sites.math.washington.edu/~rtr/papers/rtr169-VarAnalysis-RockWets.pdf: normal cone defintion

But this is confusing to me. it seems to me like the $\sum y_i a_i$ will yield a single value and not a vector. it was my understanding that the normal cone is a set of vectors.

Is my understanding wrong? Or am I misinterpreting what this book is saying for the Normal cone of a polyhedron?? thank.



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