On the generic properties of convex optimization problems in conic form

On the generic properties of convex optimization problems in conic form

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Article ID: iaor2002424
Country: Germany
Volume: 89
Issue: 3
Start Page Number: 449
End Page Number: 457
Publication Date: Jan 2001
Journal: Mathematical Programming
Authors: ,
Abstract:

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 strictly larger Hausdorff dimension than the set of data that does not. Our proof is elementary and it employs an important result due to Larman on the boundary structure of convex bodies.

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