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Volumn 61, Issue 1, 2012, Pages 35-65

Regularity conditions via generalized interiority notions in convex optimization: New achievements and their relation to some classical statements

Author keywords

convex optimization; Fenchel duality; Lagrange duality; perturbation theory; quasi interior; quasi relative interior

Indexed keywords


EID: 84856817068     PISSN: 02331934     EISSN: 10294945     Source Type: Journal    
DOI: 10.1080/02331934.2010.505649     Document Type: Article
Times cited : (42)

References (47)
  • 1
    • 33745437485 scopus 로고    scopus 로고
    • Lower semicontinuous regularization for vector-valued mappings
    • Aït Mansour, M, Metrane, A and Théra, M. 2006. Lower semicontinuous regularization for vector-valued mappings. J. Global Optim., 35: 283-309.
    • (2006) J. Global Optim. , vol.35 , pp. 283-309
    • Aït Mansour, M.1    Metrane, A.2    Théra, M.3
  • 2
    • 62249126332 scopus 로고    scopus 로고
    • Duality gap of the conic convex constrained optimization problems in normed spaces
    • Ban, LQ and Song, W. 2009. Duality gap of the conic convex constrained optimization problems in normed spaces. Math. Program., 119: 195-214.
    • (2009) Math. Program. , vol.119 , pp. 195-214
    • Ban, L.Q.1    Song, W.2
  • 3
    • 54049087423 scopus 로고    scopus 로고
    • Extended monotropic programming and duality
    • Bertsekas, DP. 2008. Extended monotropic programming and duality. J. Optim. Theor. Appl., 139: 209-225.
    • (2008) J. Optim. Theor. Appl. , vol.139 , pp. 209-225
    • Bertsekas, D.P.1
  • 4
    • 23744451353 scopus 로고    scopus 로고
    • Notions of relative interior in Banach spaces
    • Borwein, JM and Goebel, R. 2003. Notions of relative interior in Banach spaces. J. Math. Sciences, 115: 2542-2553.
    • (2003) J. Math. Sciences , vol.115 , pp. 2542-2553
    • Borwein, J.M.1    Goebel, R.2
  • 6
    • 0026867929 scopus 로고
    • Partially finite convex programming, part I: Quasi relative interiors and duality theory
    • Borwein, JM and Lewis, AS. 1992. Partially finite convex programming, part I: Quasi relative interiors and duality theory. Math. Program., 57: 15-48.
    • (1992) Math. Program. , vol.57 , pp. 15-48
    • Borwein, J.M.1    Lewis, A.S.2
  • 7
    • 85037794629 scopus 로고    scopus 로고
    • Compactly epi-Lipschitzian convex sets and functions in normed spaces
    • Borwein, JM, Lucet, Y and Mordukhovich, B. 2000. Compactly epi-Lipschitzian convex sets and functions in normed spaces. J. Convex Anal., 7: 375-393.
    • (2000) J. Convex Anal. , vol.7 , pp. 375-393
    • Borwein, J.M.1    Lucet, Y.2    Mordukhovich, B.3
  • 8
    • 77949571044 scopus 로고    scopus 로고
    • Conjugate Duality in Convex Optimization
    • Berlin, Heidelberg: Springer-Verlag
    • Boţ, RI. 2010. "Conjugate Duality in Convex Optimization". In Lecture Notes in Economics and Mathematical Systems, Vol. 637, Berlin, Heidelberg: Springer-Verlag.
    • (2010) Lecture Notes in Economics and Mathematical Systems , vol.637
    • Boţ, R.I.1
  • 9
    • 51449103147 scopus 로고    scopus 로고
    • Revisiting some duality theorems via the quasirelative interior in convex optimization
    • Boţ RI, Csetnek, ER and Moldovan, A. 2008. Revisiting some duality theorems via the quasirelative interior in convex optimization. J. Optim. Theor. Appl., 139: 67-84.
    • (2008) J. Optim. Theor. Appl. , vol.139 , pp. 67-84
    • Boţ, R.I.1    Csetnek, E.R.2    Moldovan, A.3
  • 10
    • 61349122119 scopus 로고    scopus 로고
    • Regularity conditions via quasi-relative interior in convex programming
    • Boţ, RI, Csetnek, ER and Wanka, G. 2008. Regularity conditions via quasi-relative interior in convex programming. SIAM J. Optim., 19: 217-233.
    • (2008) SIAM J. Optim. , vol.19 , pp. 217-233
    • Boţ, R.I.1    Csetnek, E.R.2    Wanka, G.3
  • 11
    • 34548654625 scopus 로고    scopus 로고
    • On strong and total Lagrange duality for convex optimization problems
    • Boţ, RI, Grad, S-M and Wanka, G. 2008. On strong and total Lagrange duality for convex optimization problems. J. Math. Anal. Appl., 337: 1315-1325.
    • (2008) J. Math. Anal. Appl. , vol.337 , pp. 1315-1325
    • Boţ, R.I.1    Grad, S.-M.2    Wanka, G.3
  • 12
    • 30944465215 scopus 로고    scopus 로고
    • An alternative formulation for a new closed cone constraint qualification
    • Boţ, RI and Wanka, G. 2006. An alternative formulation for a new closed cone constraint qualification. Nonlinear Anal.: Theor., Meth. Appl., 64: 1367-1381.
    • (2006) Nonlinear Anal.: Theor., Meth. Appl. , vol.64 , pp. 1367-1381
    • Boţ, R.I.1    Wanka, G.2
  • 13
    • 33645961296 scopus 로고    scopus 로고
    • A weaker regularity condition for subdifferential calculus and Fenchel duality in infinite dimensional spaces
    • Boţ, RI and Wanka, G. 2006. A weaker regularity condition for subdifferential calculus and Fenchel duality in infinite dimensional spaces. Nonlinear Anal.: Theor., Meth. Appl., 64: 2787-2804.
    • (2006) Nonlinear Anal.: Theor., Meth. Appl. , vol.64 , pp. 2787-2804
    • Boţ, R.I.1    Wanka, G.2
  • 14
    • 27244447811 scopus 로고    scopus 로고
    • A new geometric condition for Fenchel's duality in infinite dimensional spaces
    • Burachik, RS and Jeyakumar, V. 2005. A new geometric condition for Fenchel's duality in infinite dimensional spaces. Math. Program., 104: 229-233.
    • (2005) Math. Program. , vol.104 , pp. 229-233
    • Burachik, R.S.1    Jeyakumar, V.2
  • 16
    • 17444385638 scopus 로고    scopus 로고
    • Separation theorem based on the quasirelative interior and application to duality theory
    • Cammaroto, F and Di Bella, B. 2005. Separation theorem based on the quasirelative interior and application to duality theory. J. Optim. Theor. Appl., 125: 223-229.
    • (2005) J. Optim. Theor. Appl. , vol.125 , pp. 223-229
    • Cammaroto, F.1    Di Bella, B.2
  • 17
    • 38049125699 scopus 로고    scopus 로고
    • On a separation theorem involving the quasi-relative interior
    • Cammaroto, F and Di Bella, B. 2007. On a separation theorem involving the quasi-relative interior. Proc. Edin. Math. Soc. (2), 50: 605-610.
    • (2007) Proc. Edin. Math. Soc. , vol.50 , Issue.2 , pp. 605-610
    • Cammaroto, F.1    Di Bella, B.2
  • 20
    • 34249061432 scopus 로고    scopus 로고
    • General infinite dimensional duality and applications to evolutionary network equilibrium problems
    • Daniele, P and Giuffrè, S. 2007. General infinite dimensional duality and applications to evolutionary network equilibrium problems. Optim. Lett., 1: 227-243.
    • (2007) Optim. Lett. , vol.1 , pp. 227-243
    • Daniele, P.1    Giuffrè, S.2
  • 21
    • 84872628966 scopus 로고    scopus 로고
    • Infinite dimensional duality and applications
    • Daniele, P, Giuffrè, S, Idone, G and Maugeri, A. 2007. Infinite dimensional duality and applications. Math. Ann., 339: 221-239.
    • (2007) Math. Ann. , vol.339 , pp. 221-239
    • Daniele, P.1    Giuffrè, S.2    Idone, G.3    Maugeri, A.4
  • 23
    • 73249145584 scopus 로고    scopus 로고
    • Constraint qualifications for extended Farkas's lemmas and Lagrangian dualities in convex infinite programming
    • Fang, DH, Li, C and Ng, KF. 2009. Constraint qualifications for extended Farkas's lemmas and Lagrangian dualities in convex infinite programming. SIAM J. Optim., 20: 1311-1332.
    • (2009) SIAM J. Optim. , vol.20 , pp. 1311-1332
    • Fang, D.H.1    Li, C.2    Ng, K.F.3
  • 24
    • 34848856368 scopus 로고    scopus 로고
    • Constrained optimization and image space analysis, volume 1: separation of sets and optimality conditions
    • New York: Springer
    • Giannessi, F. 2005. "Constrained optimization and image space analysis, volume 1: separation of sets and optimality conditions". In in Mathematical Concepts and Methods in Science and Engineering, Vol. 49, New York: Springer.
    • (2005) In Mathematical Concepts and Methods in Science and Engineering , vol.49
    • Giannessi, F.1
  • 25
    • 0025462417 scopus 로고
    • A comparison of constraint qualifications in infinite-dimensional convex programming
    • Gowda, MS and Teboulle, M. 1990. A comparison of constraint qualifications in infinite-dimensional convex programming. SIAM J. Cont. Optim., 28: 925-935.
    • (1990) SIAM J. Cont. Optim. , vol.28 , pp. 925-935
    • Gowda, M.S.1    Teboulle, M.2
  • 27
    • 34648867053 scopus 로고    scopus 로고
    • A new closed cone constraint qualification for convex optimization
    • Sydney, Australia: University of New South Wales
    • Jeyakumar, V, Dinh, N and Lee, GM. 2004. "A new closed cone constraint qualification for convex optimization". In Appl. Math. Rep. AMR 04/8, Sydney, Australia: University of New South Wales.
    • (2004) Appl. Math. Rep. AMR 04/8
    • Jeyakumar, V.1    Dinh, N.2    Lee, G.M.3
  • 28
    • 70450277572 scopus 로고    scopus 로고
    • Necessary and sufficient conditions for S-lemma and nonconvex quadratic optimization
    • Jeyakumar, V, Huy, NQ and Li, G. 2009. Necessary and sufficient conditions for S-lemma and nonconvex quadratic optimization. Optim. Eng., 10: 491-503.
    • (2009) Optim. Eng. , vol.10 , pp. 491-503
    • Jeyakumar, V.1    Huy, N.Q.2    Li, G.3
  • 29
    • 42149160025 scopus 로고    scopus 로고
    • Complete characterizations of stable Farkas' lemma and cone-convex programming duality
    • Jeyakumar, V and Lee, GM. 2008. Complete characterizations of stable Farkas' lemma and cone-convex programming duality. Math. Program., 114: 335-347.
    • (2008) Math. Program. , vol.114 , pp. 335-347
    • Jeyakumar, V.1    Lee, G.M.2
  • 30
    • 72149085465 scopus 로고    scopus 로고
    • New dual constraint qualifications characterizing zero duality gaps of convex programs and semidefinite programs
    • Jeyakumar, V and Li, G. 2009. New dual constraint qualifications characterizing zero duality gaps of convex programs and semidefinite programs. Nonlinear Anal., 72: e2239-e2249.
    • (2009) Nonlinear Anal. , vol.72
    • Jeyakumar, V.1    Li, G.2
  • 31
    • 68049121845 scopus 로고    scopus 로고
    • Stable zero duality gaps in convex programming: Complete dual characterizations with applications to semidefinite programs
    • Jeyakumar, V and Li, G. 2009. Stable zero duality gaps in convex programming: Complete dual characterizations with applications to semidefinite programs. J. Math. Anal. Appl., 360: 156-167.
    • (2009) J. Math. Anal. Appl. , vol.360 , pp. 156-167
    • Jeyakumar, V.1    Li, G.2
  • 32
    • 0026867587 scopus 로고
    • Generalizations of Slater's constraint qualification for infinite convex programs
    • Jeyakumar, V and Wolkowicz, H. 1992. Generalizations of Slater's constraint qualification for infinite convex programs. Math. Program. Series B, 57: 85-101.
    • (1992) Math. Program. Series B , vol.57 , pp. 85-101
    • Jeyakumar, V.1    Wolkowicz, H.2
  • 33
    • 70450199401 scopus 로고    scopus 로고
    • Stable and total Fenchel duality for convex optimization problems in locally convex spaces
    • Li, C, Fang, D, López, G and López, MA. 2009. Stable and total Fenchel duality for convex optimization problems in locally convex spaces. SIAM J. Optim., 20: 1032-1051.
    • (2009) SIAM J. Optim. , vol.20 , pp. 1032-1051
    • Li, C.1    Fang, D.2    López, G.3    López, M.A.4
  • 34
    • 70350074661 scopus 로고    scopus 로고
    • Qualification-free optimality conditions for convex programs with separable inequality constraints
    • Li, G and Jeyakumar, V. 2009. Qualification-free optimality conditions for convex programs with separable inequality constraints. J. Convex Anal., 16: 845-856.
    • (2009) J. Convex Anal. , vol.16 , pp. 845-856
    • Li, G.1    Jeyakumar, V.2
  • 35
    • 69649083493 scopus 로고    scopus 로고
    • On extension of Fenchel duality and its application
    • Li, G and Ng, KF. 2008. On extension of Fenchel duality and its application. SIAM J. Optim., 19: 1489-1509.
    • (2008) SIAM J. Optim. , vol.19 , pp. 1489-1509
    • Li, G.1    Ng, K.F.2
  • 38
    • 0039088691 scopus 로고
    • Fenchel and Lagrange duality are equivalent
    • Magnanti, TL. 1974. Fenchel and Lagrange duality are equivalent. Math. Program., 7: 253-258.
    • (1974) Math. Program. , vol.7 , pp. 253-258
    • Magnanti, T.L.1
  • 39
    • 0009119348 scopus 로고
    • Semi-continuous mappings in general topology
    • Penot, J-P and Théra, M. 1982. Semi-continuous mappings in general topology. Archiv der Mathematik, 38: 158-166.
    • (1982) Archiv der Mathematik , vol.38 , pp. 158-166
    • Penot, J.-P.1    Théra, M.2
  • 40
    • 84856839617 scopus 로고
    • Conference Board of the Mathematical Sciences Regional Conference Series in Applied Mathematics 16, Society for Industrial and Applied Mathematics, Philadelphia
    • R.T. Rockafellar, Conjugate Duality and Optimization, Conference Board of the Mathematical Sciences Regional Conference Series in Applied Mathematics 16, Society for Industrial and Applied Mathematics, Philadelphia, 1974.
    • (1974) Conjugate Duality and Optimization
    • Rockafellar, R.T.1
  • 41
    • 27244448908 scopus 로고
    • The Fenchel duality theorem in Fréchet spaces
    • Rodrigues, B. 1990. The Fenchel duality theorem in Fréchet spaces. Optimization, 21: 13-22.
    • (1990) Optimization , vol.21 , pp. 13-22
    • Rodrigues, B.1
  • 43
    • 0031281277 scopus 로고    scopus 로고
    • Generalized semicontinuity and existence theorems for cone saddle points
    • Tanaka, T. 1997. Generalized semicontinuity and existence theorems for cone saddle points. Appl. Math. Optimmization, 36: 313-322.
    • (1997) Appl. Math. Optimmization , vol.36 , pp. 313-322
    • Tanaka, T.1
  • 44
    • 38249007206 scopus 로고
    • The convexity of A and B assures intA + B = int(A + B)
    • Tanaka, T and Kuroiwa, D. 1993. The convexity of A and B assures intA + B = int(A + B). Appl. Math. Lett., 6: 83-86.
    • (1993) Appl. Math. Lett. , vol.6 , pp. 83-86
    • Tanaka, T.1    Kuroiwa, D.2
  • 45
    • 45749111441 scopus 로고    scopus 로고
    • Some convex programs without a duality gap
    • Tseng, P. 2009. Some convex programs without a duality gap. Math. Program., 116: 553-578.
    • (2009) Math. Program. , vol.116 , pp. 553-578
    • Tseng, P.1
  • 46
    • 4243384962 scopus 로고    scopus 로고
    • A comparison of constraint qualifications in infinite-dimensional convex programming revisited
    • Zǎlinescu, C. 1999. A comparison of constraint qualifications in infinite-dimensional convex programming revisited. J. Australian Math. Soc. Series B, 40: 353-378.
    • (1999) J. Australian Math. Soc. Series B , vol.40 , pp. 353-378
    • Zǎlinescu, C.1


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