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Optimization
A Journal of Mathematical Programming and Operations Research
Volume 36, 1996 - Issue 2
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Original Articles

∊-Variational inequalities in partially ordered spaces

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Pages 105-118 | Published online: 20 Mar 2007

References

  • Aubin , J.P. and Ekeland , I. 1984 . Applied Nonlinear Analysis , New York : John Wiley .
  • Benker , H. and Kossert , S. 1982 . Remarks on quadratic optimal control problems in Hilbert spaces . Zeitschrift für Analysis und ihre Anwendungen , 1 ( 3 ) : 13 – 21 .
  • Blum , E. and Oettli , W. 1975 . Mathematische Optimierung , Springer-Verlag .
  • Borwein , J. 1982 . Continuity and differentiability properties of convex operators . Proc. London Math. Soc , 44 : 420 – 444 .
  • Brumelle , S. 1981 . Duality for multiple objective convex programs, Mathematics of Operations Research , 6 ( 2 ) : 159 – 172 .
  • Borwein , J. 1982 . Continuity and differentiability properties of convex operators . Proc. London Math. Soc , 43 ( 2 ) : 420 – 444 .
  • Bronsted , A. and Rockafellar , R.T. 1965 . On the subdifferentiability of convex functions . Proc. Amer. Math. Soc , 16 ( 2 ) : 605 – 611 .
  • Chen , G.Y. and Cheng , G.M. 1986 . “ Vector variational inequality and vector optimization ” . In Lecture Notes in Econ. and Math Syst , Edited by: Sawaragi , Y. , Inoue , K. and Nakayama , H. Vol. 1 , Berlin, New York : Springer-Verla . Interactive and lnteligent Decrsion Support Systems Heidelberg
  • Chen , G.Y. and Craven , B.D. 1990 . A Vector Variational Inequality and Optimization Over an Efficient Set . ZOR-Methods and Modells of Opeations Research , 34 : 1 – 12 .
  • Dentschev , D. and Helbig , S. 1994 . On several for ∊-efficiency. OR Spektrum , 16 : 179 – 186 . Compare also On variational principles in vector optimization. Lecture on the 4th Workshop Multicriteria Decision, Holzhau 1994. Germany
  • Durier , R. 1990 . On Pareto Optima, the Fermat –Weber Problem and Polyhedral Gauges . Mathematical Programming , 47 : 65 – 79 .
  • Durier , R. and Michelot , C. 1985 . Geometrical Properties of the Fermat-Weber Problem . European Journal of Operational Research , 20 : 332 – 343 .
  • Elster , K.H. and Elster , R. . Vector Variational Inequality and Geometric Vector Optimization . Variational Inequalities and Network Equilibrium Problems. Proc. of Conf. Erice/Sicily . June 19-25 1994 . Edited by: Giannessi , Ln F. and Maugeri , A. London : Plenum Publishing Corporation .
  • Ekeland , I. 1974 . On the variational principle . J. Math. Anal. Appl , 47 : 324 – 353 .
  • Gerstewitz (Tammer), Chr . 1987 . Näherungslösungen in der Vektoroptimierung. Seminarbericht , Vol. 90 , 67 – 76 . Berlin : Humboldt-Universität .
  • 1989 . Notwendige Bedingungen für effziente und ∊-effiziente Elemente bei Vektorminimumproblemen , 5 : 82 – 89 . Wissenschaftliche Schriftenreihe der TU Karl Marx-Stadt
  • Weidner , P. 1990 . Nonconvex separation theorems and some applications in vector optimization . J . Optim. Theory Appl , 67 ( 2 ) : 297 – 320 .
  • Göpfert , A. and Nehse , R. 1990 . “ Verfahren und Anwendungen ” . In Vektoroptimierung - Theorie , Teubner Verlagsgesellschaft . BSB B.G
  • Idrissi , H. , Lefebvre , O. and Michelot , C. 1988 . A Primal-Dual Algorithm for a Constrained Fermat - Weber Problem Involving Mixed Norms . Recherche operationnelle/Operations Research , 22 : 313 – 330 .
  • Idrissi , H. , Loridan , P. and Michelot , C. 1988 . Approximation of Solutions for Location Problems . Journ. Opt. Theory Appl , 56 : 127 – 143 .
  • Isac G. A variant of Ekeland's principle for Pareto ∊ - efficiency 1994 In preparation
  • Jahn , G. 1986 . Mathematical Vector Optimization in Partially Ordered Spaces , Bern, New York : Lang Verlag Frankfurt .
  • Khanh , P.Q. 1986 . On Caristi–Kirk's theorem and Ekeland's variational principle for Pareto extrema. lnstitude of Mathematics , Polich Academy of Sciences . Preprint
  • Kuhn , H.W. 1973 . A Note on Fermat's Problem. Mathematical Programming , 4 : 98 – 107 .
  • Loridan , P. 1984 . ∊-solutions in vector minimization problems . J. Optim. Theory Appl , 43 ( 2 ) : 265 – 276 .
  • Luc , D.T. 1989 . Theory of Vector Optimization , Berlin : Springer Verlag . Heidelberg
  • Mancino , O.G. and Stempacchia , G. 1972 . Convex programming and variational in equalities . J. Optim. Theory and Appl , 9 ( 1 ) : 3 – 23 .
  • Nemeth , A.B. 1986 . A Nonconvex Vector Minimization Problem . Nonlin. Anal. Theory , 10 ( 7 ) : 669 – 678 . Methods and Applicaitons
  • Oettli , W. 1977 . Approximate solutions of variational inequalities , Edited by: Helmstädter , E. and Henn , R. 535 – 538 . Tüibingen : Verlag J.C.B. Mohr . Quantitative Wirtschaftsforschung
  • Phelps , J.P. 1989 . “ Convex Functions. Monotone Operators and Differentiability ” . In Lecture Notes in Mathematics 1364 , Berlin, New York : Springer Verlag . Heidelberg
  • Staib , T. 1988 . On generalizations of Pareto minimality . J. Optim. Theory Appl , 59 : 289 – 306 .
  • Tammer Chr Charakterisierung effizienter Elemente von Vektoroptimierungsaufgaben Habilitationsschrift Merseburg 1991
  • Tammer , Chr. 1992 . A gerneralization of Ekeland's variational principle . Optimization , 25 : 129 – 141 .
  • Tammer , Chr. 1992 . Existence resulrs and necessary conditions for ∊-efficient elements . Multicriteria Decision Proceedings of the 14 rh Meeting of the German Working Group Mehrkriterielle Entsch . 1992 . Edited by: Brosowski , B. , Esther , J. , Helbig , S. and Nehse , R. pp. 97 – 110 . Frankfurt : Lang Verlag . Main Bern
  • Tammer , Chr. 1993 . Erweiterungen und Anwendungen des Variationsprinzips von Ekeland . ZAMM, Z. angew. Marh. Mech , 73 ( 7 ) : 832 – 826 . 8
  • Tammer , Chr. . Necessary conditions for approximately efficient solutions of vector approximation . Proceedings DGOR/NGOR Conf . Amsterdam.
  • Valyi , I. 1986 . On approximate vector optimization , IlASA Laxenburg . Working Paper 86-7
  • Wanka G. Kolmogorov Condltlons for Vectorial Approximation Problems 1994 To appear in: OR Spektrum
  • Wendell , R.E. , Hurter , A.P. and Lowe , T.J. 1973 . Efficient Points in Location Problems . AIEE Transactions , 9 : 238 – 246 .
  • Yang , X.Q. 1993 . Vector variational inequality and its duality. Nonlinear Analysis . Theory Methods and Applications , 21 ( 11 ) : 869 – 877 .

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