A note on strong duality in convex semidefinite optimization: Necessary and sufficient conditions

Optimization Letters

Volumn 2, Issue 1, 2008, Pages 15-25

  Jeyakumar, V ^a  

^a UNIVERSITY OF NEW SOUTH WALES   (Australia)

Author keywords

Constraint qualifications; Convex programming; Semidefinite optimization; Strong duality

Indexed keywords

APPROXIMATION THEORY; COMPUTER SIMULATION; CONSTRAINT THEORY; ERROR ANALYSIS; LAGRANGE MULTIPLIERS; PROBLEM SOLVING;

CONICAL HULL INTERSECTION PROPERTY (CHIP); CONSTRAINT QUALIFICATIONS; CONVEX OPTIMIZATION; CONVEX PROGRAMMING; OPTIMAL VALUES; SEMIDEFINITE OPTIMIZATION; STRONG DUALITY; ZERO DUALITY GAP;

OPTIMIZATION;

EID: 35448976508     PISSN: 18624472     EISSN: 18624480     Source Type: Journal    
DOI: 10.1007/s11590-006-0038-x     Document Type: Article

References (23)

1. Balakrishnan V. and Vandenberghe L. (2003). Semidefinite programming duality and linear time-invariant systems. IEEE Trans. Autom. Control 48: 30-41
2. Borwein J.M. and Lewis A.S. (1992). Partially finite convex programming, part I: Quasi relative interiors and duality theory. Math. Progr. 57: 15-48
3. Boyd, S., El Ghaoui, L., Feron, E., Balakrishnan, V.: Linear matrix inequalities in systems and control theory. In: SIAM Stud. Appl. Math., vol. 15. SIAM, Philadelphia (1994)
4. Boyd S. and Vandenberghe L. (2004). Convex Optimization. Cambridge University Press, Cambridge
5. Burachik R.S. and Jeyakumar V. (2005). A simple closure condition for the normal cone intersection formula. Proc. Am. Math. Soc. 133: 1741-1748
6. Burachik R.S. and Jeyakumar V. (2005). A new geometric condition for Fenchel's duality in infinite dimensional spaces. Math. Program. Ser. B 104: 229-233
7. Burachik R.S., Jeyakumar V. and Wu Z.Y. (2006). Necessary and sufficient conditions for stable conjugate duality. Nonlin. Anal. 64: 1998-2006
8. Deutsch F. (1998). The role of conical hull intersection property in convex optimization and approximation. In: Chui, C.K. and Schumaker, L.L. (eds) Approximation Theory, vol. IX, pp. Vanderbilt University Press, Nashville
9. Deutsch F., Li W. and Swetits J. (1999). Fenchel duality and the strong conical hull intersection property. J. Optim. Theory Appl. 102: 681-695
10. Guignard M. (1969). Generalized Kuhn-Tucker conditions for mathematical programming problems in a Banach space. SIAM J. Control 7: 232-241
11. Helmberg C. (2002). Semidefinite programming. Eur. J. Oper. Res. 137: 461-482
12. Hiriart-Urruty J-B. and Lemarechal C. (1993). Convex Analysis and Minimization Algorithms vols. I, II. Springer, Heidelberg
13. Jeyakumar V. (2006). The strong conical hull intersection property for convex programming. Math. Progr. Ser. A 106: 81-92
14. Jeyakumar V. and Nealon M. (2000). Complete characterizations of optimality for convex semidefinite programming. Can. Math. Soc. Conf. Proc 27: 165-173
15. Jeyakumar V. and Wolkowicz H. (1992). Generalizations of Slater's constraint qualification for infinite convex programs. Math. Progr. 57: 85-102
16. Jeyakumar V., Lee G.M. and Dinh N. (2003). New sequential Lagrange multiplier conditions characterizing optimality without constraint qualification for convex programs. SIAM J. Optim. 14: 534-547
17. De Oliveira M.C. (2004). Investigating duality on stability conditions. Syst. Control Lett. 52: 1-6
18. Ramana M.V. (1997). An exact duality theory for semidefinite programming and its complexity implications. Math. Progr. 77: 129-162
19. Ramana M.V., Tunçcel L. and Wolkowicz H. (1997). Strong duality for semidefinite programming. SIAM J. Optim. 7: 644-662
20. Shapiro, A.: On duality theory of conic linear problems, semi-infinite programming (Alicante, 1999). In: Nonconvex Optim. Appl. vol. 57, pp. 135-165. Kluwer, Dordrecht (2001)
21. Todd M.J. (2001). Semidefinite optimization. Acta Numer. 10: 515-560
22. Vandenberghe L. and Boyd S. (1996). Semidefinite programming. SIAM Rev. 38: 49-95
23. Wolkowicz, H., Saigal, R., Vandenberghe, L.: Handbook of semidefinite programming. In: International Series in Operations Research and Management Science, vol. 27. Kluwer, Dordrecht (2000)