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Optimization
A Journal of Mathematical Programming and Operations Research
Volume 61, 2012 - Issue 5
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Original Articles

Second-order invex functions in nonlinear programming

Vsevolod Ivanov Ivanov Department of Mathematics, Technical University of Varna, 9010 Varna, BulgariaCorrespondence[email protected]
Pages 489-503 | Received 09 Jan 2010, Accepted 16 Jul 2010, Published online: 14 Oct 2010

References

  • Antczak , T . 2007 . A modified objective function method in mathematical programming with second order invexity . Numer. Funct. Anal. Optim. , 28 : 1 – 12 .
  • Bector , CR and Bector , BK . 1985 . (Generalized)-bonvex functions and second-order duality for nonlinear programming problem . Congr. Numer. , 52 : 37 – 52 .
  • Ben-Israel , A and Mond , B . 1986 . What is invexity? . J. Aust. Math. Soc. Ser. B , 28 : 1 – 9 .
  • Ginchev , I and Ivanov , VI . 2007 . “ Higher-order pseudoconvex functions ” . In Lecture Notes in Economics and Mathematical Systems, Vol. 583 , Edited by: Konnov , IV , Luc , DT and Rubinov , AM . 247 – 264 . Berlin, Heidelberg, New York : Springer .
  • Ginchev , I and Ivanov , VI . 2008 . Second-order optimality conditions for problems with C 1 data . J. Math. Anal. Appl. , 340 : 646 – 657 .
  • Guignard , M . 1969 . Generalized Kuhn-Tucker optimality conditions for mathematical programming problems in a Banach space . SIAM J. Control , 7 : 232 – 241 .
  • Hanson , MA . 1981 . On sufficiency of the Kuhn-Tucker conditions . J. Math. Anal. Appl. , 80 : 545 – 550 .
  • Hanson , MA . 1993 . Second order invexity and duality in mathematical programming . Opsearch , 30 : 313 – 330 .
  • Hanson , MA and Mond , B . 1987 . Necessary and sufficient conditions in constrained optimization . Math. Program. , 37 : 51 – 58 .
  • Mangasarian , OL . 1975 . Second- and higher-order duality in nonlinear programming . J. Math. Anal. Appl. , 51 : 607 – 620 .
  • Mishra , SK . 1997 . Second-order generalized invexity and duality in mathematical programming . Optimization , 42 : 51 – 69 .
  • Mishra , SK and Giorgi , G . 2008 . Invexity and Optimization , Berlin : Springer .
  • Mishra , SK and Rueda , NG . 2000 . Higher-order generalized invexity and duality in mathematical programming . J. Math. Anal. Appl. , 247 : 173 – 182 .
  • Mishra , SK and Rueda , NG . 2002 . Higher-order generalized invexity and duality in nondifferentiable mathematical programming . J. Math. Anal. Appl. , 272 : 496 – 506 .
  • Mishra , SK , Wang , SY and Lai , KK . 2009 . Generalized Convexity and Vector Optimization , Berlin : Springer .
  • Mond , B . 1974 . A class of nondifferentiable mathematical programming problems . J. Math. Anal. Appl. , 46 : 169 – 174 .
  • Mond , B . 1974 . Second-order duality for nonlinear programs . Opsearch , 11 : 90 – 99 .
  • Mond , B and Zhang , J . 1998 . “ Higher order invexity and duality in mathematical programming ” . In Nonconvex Optimization and its Applications , Edited by: Crouzeix , JP , Martinez-Legaz , JE and Volle , M . Vol. 27 , 357 – 372 . Dordrecht : Kluwer Academic .
  • Sach , PH , Kim , DS and Lee , GM . 2006 . Invexity and necessary optimality condition in nonsmooth programs . J. Korean Math. Soc. , 43 : 241 – 258 .
  • Tanaka , Y . 1990 . Note on generalized convex functions . J. Optim. Theory Appl. , 66 : 345 – 349 .

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