On the generic properties of convex optimization problems in conic form

Authors
Pataki, G Tuncel, L
Citation
G. Pataki et L. Tuncel, On the generic properties of convex optimization problems in conic form, MATH PROGR, 89(3), 2001, pp. 449-457
Citations number
20
Categorie Soggetti
Mathematics
Journal title
MATHEMATICAL PROGRAMMING
ISSN journal
00255610 → ACNP
Volume
89
Issue
3
Year of publication
2001
Pages
449 - 457
Database
ISI
SICI code
0025-5610(200102)89:3<449:OTGPOC>2.0.ZU;2-N
Abstract
We prove that strict complementarity, primal and dual nondegeneracy of opti mal solutions of convex optimization problems in conic form are generic pro perties. In this paper, we say generic to mean that the set of data possess ing the desired property (or properties) has strictly larger Hausdorff dime nsion than the set of data that does not. Our proof is elementary and it em ploys an important result due to Larman [7] on the boundary structure of co nvex bodies.