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2013 | 11 | 11 | 2020-2033
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Characterizations of ɛ-duality gap statements for constrained optimization problems

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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In this paper we present different regularity conditions that equivalently characterize various ɛ-duality gap statements (with ɛ ≥ 0) for constrained optimization problems and their Lagrange and Fenchel-Lagrange duals in separated locally convex spaces, respectively. These regularity conditions are formulated by using epigraphs and ɛ-subdifferentials. When ɛ = 0 we rediscover recent results on stable strong and total duality and zero duality gap from the literature.
Wydawca
Czasopismo
Rocznik
Tom
11
Numer
11
Strony
2020-2033
Opis fizyczny
Daty
wydano
2013-11-01
online
2013-08-23
Twórcy
Bibliografia
  • [1] Anbo Y., Nonstandard arguments and the characterization of independence in generic structures, RIMS Kôkyûroku, 2009, 1646, 4–17
  • [2] Boţ R.I., Grad S.-M., Lower semicontinuous type regularity conditions for subdifferential calculus, Optim. Methods Softw., 2010, 25(1), 37–48 http://dx.doi.org/10.1080/10556780903208977
  • [3] Boţ R.I., Grad S.-M., Wanka G., Maximal monotonicity for the precomposition with a linear operator, SIAM J. Optim., 2006, 17(4), 1239–1252
  • [4] Boţ R.I., Grad S.-M., Wanka G., Weaker constraint qualifications in maximal monotonicity, Numer. Funct. Anal. Optim., 2007, 28(1–2), 27–41
  • [5] Boţ R.I., Grad S.-M., Wanka G., A new constraint qualification for the formula of the subdifferential of composed convex functions in infinite dimensional spaces, Math. Nachr., 2008, 281(8), 1088–1107 http://dx.doi.org/10.1002/mana.200510662
  • [6] Boţ R.I., Grad S.-M., Wanka G., New regularity conditions for strong and total Fenchel-Lagrange duality in infinite dimensional spaces, Nonlinear Anal., 2008, 69(1), 323–336 http://dx.doi.org/10.1016/j.na.2007.05.021
  • [7] Boţ R.I., Grad S.-M., Wanka G., On strong and total Lagrange duality for convex optimization problems, J. Math. Anal. Appl., 2008, 337(2), 1315–1325 http://dx.doi.org/10.1016/j.jmaa.2007.04.071
  • [8] Boţ R.I., Grad S.-M., Wanka G., Duality in Vector Optimization, Vector Optim., Springer, Berlin, 2009
  • [9] Boţ R.I., Grad S.-M., Wanka G., Generalized Moreau-Rockafellar results for composed convex functions, Optimization, 2009, 58(7), 917–933 http://dx.doi.org/10.1080/02331930902945082
  • [10] Boţ R.I., Wanka G., Farkas-type results with conjugate functions, SIAM J. Optim., 2005, 15(2), 540–554 http://dx.doi.org/10.1137/030602332
  • [11] Boţ R.I., Wanka G., An alternative formulation for a new closed cone constraint qualification, Nonlinear Anal., 2006, 64(6), 1367–1381 http://dx.doi.org/10.1016/j.na.2005.06.041
  • [12] Boţ R.I., Wanka G., A weaker regularity condition for subdifferential calculus and Fenchel duality in infinite dimensional spaces, Nonlinear Anal., 2006, 64(12), 2787–2804 http://dx.doi.org/10.1016/j.na.2005.09.017
  • [13] Fang D.H., Li C., Ng K.F., Constraint qualifications for optimality conditions and total Lagrange dualities in convex infinite programming, Nonlinear Anal., 2010, 73(5), 1143–1159 http://dx.doi.org/10.1016/j.na.2010.04.020
  • [14] Friedman H.M., A way out, In: One Hundred Years of Russell’s Paradox, de Gruyter Ser. Log. Appl., 6, de Gruyter, Berlin, 2004, 49–84
  • [15] Jeyakumar V., Li G.Y., New dual constraint qualifications characterizing zero duality gaps of convex programs and semidefinite programs, Nonlinear Anal., 2009, 71(12), e2239–e2249 http://dx.doi.org/10.1016/j.na.2009.05.009
  • [16] Jeyakumar V., Li G.Y., Stable zero duality gaps in convex programming: Complete dual characterisations with applications to semidefinite programs, J. Math. Anal. Appl., 2009, 360(1), 156–167 http://dx.doi.org/10.1016/j.jmaa.2009.06.043
  • [17] Li C., Fang D., López G., López M.A., Stable and total Fenchel duality for convex optimization problems in locally convex spaces, SIAM J. Optim., 2009, 20(2), 1032–1051 http://dx.doi.org/10.1137/080734352
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Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_s11533-013-0294-9
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