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Original Articles

On a Fenchel–Young Type Conjugacy for Invex Functions

Pages 59-66 | Published online: 31 Aug 2006

References

  • Antczak , T. and Galewski , M. 2001 . On r-Invex and r-Convex Functions in Mathematical Programming Faculty of Mathematics, Lodz University . Preprint no. 05
  • Bazaara , M. S. , Sherali , H. D. and Shetty , C. M. 1991 . Nonlinear Programming. Theory and Applications J. Wiley. .
  • Ben-Israel , A. and Mond , B. 1986 . What is invexity . J. Austral. Math. Soc., Ser. B , 28 : 1 – 9 .
  • Clarke , F. H. 1984 . Nonsmooth Optimization Moscow : Nauka . (in Russian)
  • Craven , B. D . 1995 . “ Relationships between invex properties ” . In Recent Trends in Optimization Theory Edited by: Agrawal , R. P. Singapore : World Scientific .
  • Ekeland , I. and Temam , R. 1976 . Convex Analysis and Variational Problems Amsterdam, , North-Holland
  • Galewski , M. 2001 . On some connection between invex and convex problems in nonlinear programming . Control and Cybernetics , 30 ( 1 ) : 11 – 22 .
  • Galewski , M. 1999 . On a Periodic Solution to a Certain Type of Nonlinear Inclusion with Invexity Assumption Lodz : Faculty of Mathematics . Preprint no. 16
  • Hanson , M. A. 1981 . On sufficiency of the Kuhn–Tucker conditions . J. Math. Anal. Appl. , 80 : 545 – 550 .
  • Hanson , M. A. and Mond , B. 1987 . Convex transformable programming problems and invexity . J. Inf. Optim. Sci. , 8 : 201 – 207 .
  • Mangasarian , O. L . 1969 . Nonlinear Programming New-York : McGraw-Hill .
  • Mond , B. and Weir , T. 1986 . “ Concave functions and duality ” . In Concavity and Economics Edited by: Schaible , T.
  • Nowakowski , A. 1992 . A New variational principle and duality for periodic solutions of hamilton's equations . J. Differential Equations , 97 ( 1 ) : 174 – 188 .
  • Nowakowski , A. and Rogowski , A. 2001 . On the new variational principles and duality for periodic solutions of Lagrange equations with superlinear nonlinearities . J.M.A.A. , 264 : 168 – 181 .
  • Orpel , A. 1997 . Periodic solutions of differential equations and nonconvex functionals in calculus of variations . Optimization , 40 : 313 – 333 .
  • Pini , R. 1991 . Invexity and generalized convexity . Optimization , 22 : 513 – 525 .
  • Pini , R. 1994 . Convexity along curves and invexity . Optimization , 29 : 301 – 309 .
  • Reiland , T. W. 1990 . Nonsmooth invexity . Bull. Austral. Math. Soc. , 42 : 437 – 446 .
  • Rockafellar , T. R. and Wets , R. J.-B. 1998 . Variational Analysis Springer Verlag .

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