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Mathematical Programming

, Volume 89, Issue 3, pp 449–457 | Cite as

On the generic properties of convex optimization problems in conic form

  • Gábor Pataki
  • Levent Tunçel

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 [7] on the boundary structure of convex bodies.

Key words: convex optimization – strict complementarity – nondegeneracy 
Mathematics Subject Classification (1991): 90C25, 90C05, 52A41, 47D20, 90C51 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Gábor Pataki
    • 1
  • Levent Tunçel
    • 2
  1. 1.Department of IE/OR, Columbia University, New York, USA, e-mail: gabor@ieor. columbia.eduUS
  2. 2.Department of Combinatorics and Optimization, Faculty of Mathematics, University of Waterloo, Waterloo, Ontario, N2L 3G1 Canada, e-mail: ltuncel@math.uwaterloo.caCA

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