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On the generic properties of convex optimization problems in conic form

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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.

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Authors and Affiliations

  1. Department of IE/OR, Columbia University, New York, USA, e-mail: gabor@ieor. columbia.edu, , , , , , US

    Gábor Pataki

  2. Department of Combinatorics and Optimization, Faculty of Mathematics, University of Waterloo, Waterloo, Ontario, N2L 3G1 Canada, e-mail: ltuncel@math.uwaterloo.ca, , , , , , CA

    Levent Tunçel

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  1. Gábor Pataki
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  2. Levent Tunçel
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Received: September 1997 / Accepted: May 2000¶Published online November 17, 2000

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Pataki, G., Tunçel, L. On the generic properties of convex optimization problems in conic form. Math. Program. 89, 449–457 (2001). https://doi.org/10.1007/PL00011408

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  • DOI: https://doi.org/10.1007/PL00011408

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