On duality concepts in fractional programming

References

• Beoni , C. 1986 . A Generalization of Fenchels Duality-Theory . Journal of Optimization Theory and Applications , 49 ( 3 ) : 375 – 389 .
   Web of Science ®Google Scholar
• Bector , C.R. 1973 . Duality in Nonlinear Programming . Zeitschrift für Operations Research , 17 ( 3 ) : 183 – 193 .
   Google Scholar
• Bector , C.R. , Chandra , S. and Bector , M.K. 1989 . Generalized Fractional Programming, Duality. A Parametric Approach . Journal of Optimization Theory and Application , 60 ( 2 ) : 242 – 261 .
   Web of Science ®Google Scholar
• Cambini , A. and Martein , L. 1985 . On the Fenchel-like and Lagrangian Duality in Fractional Programming . Methods of Operations Research , 53 ( 2 ) : 21 – 32 .
   Google Scholar
• 1990 . “ Generalized Convexity and Fractional Programming with Economic Applications ” . In Lecture Notes in Economics and Mathematical Systems Vol. 345 ,
   Google Scholar
• Craven , B.D. “ Fractional Programming ” . In Sigma Series in Applied Mathematics , Edited by: White , D.J. Berlin : Heldermann Verlag .
   Google Scholar
• Craven , B.D. 1980 . “ Duality for generalized convex mathematical programs ” . In Generalized Concavity in Optimization and Economics , Edited by: Schaible , S. and Ziemba , W.T. 473 – 489 . New York : Academic Press .
   Google Scholar
• Deumlich , R. 1980 . Ein geometrischer Zugang zur Optimierungstheorie auf der Grundlage der Φ-konjugierten Funktionen , Pädagogische Hochschule Halle .
   Google Scholar
• Deumlich , R. and Elster , K.H. 1983 . Φ-Conjugation and Nonconvex Optimization, A Survey Part I. Math . Operationsforsch. u. Statist, Ser. Optimization , 14 ( 1 ) : 125 – 149 . Part I
   Google Scholar
• Deumlich , R. and Elster , K.H. 1984 . Φ-Conjugation and Nonconvex Optimization A Survey Part II . Math Operationsforsch. u. Statist.Ser. Optimization , 16 ( 6 ) : 499 – 515 .
   Google Scholar
• Deumlich , R. and Elster , K.H. 1985 . Φ-Conjugation and Nonconvex Optimization A Survey Part III.Math . Operationsforsch.u.Statist.Ser.Optimization , 16 ( 6 ) : 789 – 803 .
   Google Scholar
• Deumlich , R. and Elster , K.H. 1978 . Duality for Nonconvex Optimization Problems . Math.Operationsforsch. u. Statist., Ser. Optimization , 9 ( 3 ) : 335 – 347 .
   Google Scholar
• Deumlich , R. and Elster , K.H. 1980 . Duality Theorems and Optimality Conditions for Nonconvex Optimization Problems . Math. Operationsforsch. u. Statist., Ser. Optimization , 11 ( 2 ) : 181 – 219 .
   Google Scholar
• Deumlich , R. and Elster , K.H. 1982 . “ Recent Results on Φ-Conjugation and Nonconvex Optimization ” . In Operations Research in Progress , Edited by: Feichtinger , G. and Kail , P. 27 – 40 . Boston : D. Reidel Publ. Comp. Dortrecht .
   Google Scholar
• Deumlich , R. , Ester , K.H. and Nehse , R. . Survey of Mathematical Programming . Proceedings of the 9th International Mathematical Programming Symposium . 1976 , Budapest. Edited by: Prekopa , A. Vol. 1 , 9 , pp. 193 – 204 . Budapest : Akadmiai Kiado . Generalizations of Conjugate Functions, S
   Google Scholar
• Deumlich , R. and Elster , K.H. 1984 . Proceedings 9. Sympos. Operations Research . Fractional Programming in View of Generalized Conjugation . August 1984 , Osnabrück.
   Google Scholar
• Deumlich , R. and Elster , K.H. 1986 . On Perturbations of Certain Nonconvex Optimization Problems . Journal of Optimization Theory and Applications , 48 ( 1 ) August
   Web of Science ®Google Scholar
• Deumlich , R. and Ohlendorf , E. 1991 . “ Anmerkungen zur Dualität in der Quotientenopt- imierung ” . In Wissenschaftliche Zeitschrift der Ilmenau Vol. 37 , Heft
   Google Scholar
• Elster , K.H. and Deumlich , R. “ On duality for nonconvex optimization problems ” . In Proceedings V. Symposium on Operations Research
   Google Scholar
• Elster , K.H. and Deumlich , R. . Lagrange, duality for nonconvex optimization problems . Proceedings VI. Symposium on Operations Research . Augsburg.
   Google Scholar
• Fenchel , W. 1953 . “ Lectures Notes, Department of Math ” . In Convex Cones, Sets and Functions , Princeton, N.J : Princeton Univ .
   Google Scholar
• Golstein , E.G. 1975 . Dualitätstheorie in der nichtlinearen Optimierung und ihre Anwendung , Berlin : Akademie Verlag .
   Google Scholar
• Martinez-Legaz , J.E. 1988 . Quasiconvex Duality by Generalized Conjugation Methods . Math. Operationsforsch. u. Statist., Ser. Optimization , 19 : 603 – 652 .
   Google Scholar
• Schaible , S. 1976 . Fractional Programming I: Duality . Management Science , 22B : 858 – 867 .
   Google Scholar
• Singh , C. and Rueda , N. 1990 . Generalized Fractional Programming: Optimality and Duality Theory . Journal of Optimization Theory and Application , 66 ( 1 )
   Web of Science ®Google Scholar