The TolandFenchelLagrange duality of DC programs for composite convex functions
Pages: 9  23,
Issue 1,
March
2014
doi:10.3934/naco.2014.4.9 Abstract
References
Full text (393.4K)
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Yuying Zhou  Department of Mathematics, Soochow University, Suzhou, 215006, China (email)
Gang Li  School of Sciences, Zhejiang A & F University, Hangzhou 311300, China (email)
1 
L. T. H. An, An efficient algorithm for globally minimizing a quadratic function under convex quadratic constraints, Math. Program., 87 (2000), 401426. 

2 
L. T. H. An and P. D. Tao, The DC (difference of convex functions) programming and DCA revisited with DC models of real world nonconvex optimization problems, Ann. Oper. Res., 133 (2005), 2346. 

3 
J. M. Borwein and A. S. Lewis, Partially finite convex programming, part I: Quasi relative interiors and duality theory, Math. Program., 57 (1992), 1548. 

4 
R. I. Boţ, E. R. Csetnek and G. Wanka, Regularity conditions via quasirelative interior in convex programming, SIAM. J. Optim., 19 (2008), 217233. 

5 
R. I. Boţ, S. M. Grad and G. Wanka, A new constraint qualification for the formula of the subdifferential of composed convex functions in infinite dimensional spaces, Math. Nachr., 281 (2008), 10881107. 

6 
R. I. Boţ, S. M. Grad and G. Wanka, Generalized MoreauRockafellar results for composed convex functions, Optimization, 58 (2009), 917933. 

7 
R. I. Boţ, S. M. Grad and G. Wanka, On strong and total Lagrange duality for convex optimization problems, J. Math. Anal. Appl., 337 (2008), 13151325. 

8 
R. I. Boţ, I. B. Hodrea and G. Wanka, Farkastype results for inequality systems with composed convex functions via conjugate duality, J. Math. Anal. Appl., 322 (2006), 316328. 

9 
R. I. Boţ and G. Wanka, A weaker regularity condition for subdifferential calculus and Fenchel duality in infinite dimensional spaces, Nonlinear Anal., 64 (2006), 27872804. 

10 
R. I. Boţ and G. Wanka, An alternative formulation for a new closed cone constraint qualification, Nonlinear Anal., 64 (2006), 13671381. 

11 
R. S. Burachik and V. Jeyakumar, A dual condition for the convex subdifferential sum formula with applications, J. Convex Anal., 12 (2005), 279290. 

12 
R. S. Burachik and V. Jeyakumar, A new geometric condition for Fenchel duality in infinite dimensional spaces, Math. Program., 104 (2005), 229233. 

13 
B. D. Craven, Mathematical Programming and Control Theory, Chapman and Hall, London, 1978. 

14 
N. Dinh, M. A. Goberna and M. A. López, From linear to convex systems: consistency, Farkas lemma and applications, J. Convex Anal., 13 (2006), 113133. 

15 
N. Dinh, M. A. Goberna and M. A. López and T. Q. Son, New Farkastype constraint qualifications in convex infinite programming, ESAIM Control Optim. Calc. Var., 13 (2007), 580597. 

16 
N. Dinh, T. T. A. Nghia and G. Vallet, A closedness condition and its applications to DC programs with convex constraints, Optimization, 59 (2010), 541560. 

17 
N. Dinh, G. Vallet and T. T. A. Nghia, Farkastype results and duality for DC programs with convex constraints, J. Convex Anal., 15 (2008), 253262. 

18 
D. H. Fang, C. Li and X. Q. Yang, Stable and total Fenchel duality for DC optimization problems in locally convex spaces, SIAM J. Optim., 21 (2011), 730760. 

19 
S. P. Fitzpatrick and S. Simons, The conjugates, compositions and marginals of convex functions, J. Convex Anal., 8 (2001), 423446. 

20 
M. S. Gowda and M. Teboulle, A comparison of constraint qualifications in infinite dimensional convex programming, SIAM J. Control Optim., 28 (1990), 925935. 

21 
C. Li, D. H. Fang, G. López and M. A. López, Stable and total Fenchel duality for convex optimization problems in locally convex spaces, SIAM, J. Optim., 20 (2009), 10321051. 

22 
C. Li, F. Ng and T. K. Pong, The SECQ, linear regularity and the strong CHIP for infinite system of closed convex sets in normed linear space, SIAM J. Optim., 18 (2007), 643665. 

23 
G. Li, X. Q. Yang and Y. Y. Zhou, Stable strong and total parametrized dualities for DC optimization problems in locally convex spaces, J. Ind. Manag. Optim., 9 (2013), 669685. 

24 
J. F. Toland, Duality in nonconvex optimization, J. Math. Anal. Appl., 66 (1978), 399415. 

25 
H. Tuy, Convex Analysis and Global Optimization, Kluwer Academic Publishers, Dordrecht, 1998. 

26 
C. Zălinescu, Convex Analysis in General Vector Space, World Sciencetific Publishing, Singapore, 2002. 

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