On the primal-dual geometry of level sets in linear and conic optimization

SIAM Journal on Optimization

Volumn 13, Issue 4, 2003, Pages 1004-1013

  Freund, Robert M ^a  

^a MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

Conic optimization; Convex optimization; Duality; Level sets

Indexed keywords

EID: 0242679721     PISSN: 10526234     EISSN: None     Source Type: Journal    
DOI: 10.1137/S1052623401393645     Document Type: Article

References (7)

1. A. BEN-ISRAEL, A. CHARNES, AND K. O. KORTANEK, Duality and asymptotic solvability over cones, Bull. Amer. Math. Soc., 75 (1969), pp. 318-324.
2. R. J. DUFFIN, Infinite Programs, Ann. of Math. Stud. 38, H.W. Kuhn and A.W. Tucker, eds., Princeton University Press, Princeton, NJ, 1956, pp. 157-170.
3. R. M. FREUND AND J. R. VERA, Condition-based complexity of convex optimization in conic linear form via the ellipsoid algorithm, SIAM J. Optim., 10 (1999), pp. 155-176.
4. R. M. FREUND AND J. R. VERA, Some characterizations and properties of the "distance to ill-posedness" and the condition measure of a conic linear system, Math. Program., 86 (1999), pp. 225-260.
5. J. L. GOFFIN, The relaxation method for solving systems of linear inequalities, Math. Oper. Res., 5 (1980), pp. 388-414.
6. Y. NESTEROV AND A. NEMIROVSKII, Interior Point Polynomial Algorithms in Convex Programming, SIAM, Philadelphia, 1994.
7. S. J. WRIGHT, Primal-Dual Interior-Point Methods, SIAM, Philadelphia, 1997.