On the generic properties of convex optimization problems in conic form

@article{Pataki2001OnTG,
  title={On the generic properties of convex optimization problems in conic form},
  author={G{\'a}bor Pataki and Levent Tunçel},
  journal={Math. Program.},
  year={2001},
  volume={89},
  pages={449-457}
}
We prove that strict complementarity, primal and dual nondegeneracy of optimal solutions of convex optimization problems in conic form are generic properties. In this paper, we say generic to mean that the set of data possessing the desired property (or properties) has the same Hausdorr measure as the set of data that does not. Our proof is elementary and it employs an important result due to Larman 7] on the boundary structure of convex bodies. 

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