References
- Ashton , D.J. and Atkins , D.R. 1979 . Multicriteria programming for financial planning . J. Oper. Res , 30 : 259 – 270 .
- Barrodale , I. 1973 . Best rational approximation and strict quasiconvexity . SIAM J. Numer. Anal , 10 : 8 – 12 .
- Barrodale , I. , Powell , M.J.D. and Roberts , F.D.K. 1972 . The diflerential correction algorithm for rational lx -approximation . SIAM .I. Numer. Anal , 9 : 493 – 504 .
- Bector , C.R. , Chandra , S. and Bector , M.K. 1989 . Generalized fractional programming: A parametric approach . J. Optim. Theory Appl , 60 : 243 – 260 .
- Bector , C.R. and Suneja , S.K. 1988 . Duality in nondifferentiable generalized fractional programming . Asia-Pacific. J. Oper. Res , 5 : 134 – 139 .
- Bcctor , M.K. , Husain , I. , Chandra , S. and Bector , C.R. 1988 . A duality model for a generalized minmax program . Naval Res. Logist , 35 : 493 – 501 .
- Benadada , Y. , Crouzeix , J.P. and Ferland , J.A. 1990 . “ An interval-type algorithm for generalized fractional programming ” . In Generalized Convexity and Fractional Programming with Economic Applications Lecture Notes in Economics and Mathematical Systems , Vol. 345 , 106 – 120 . Berlin : Springer-Verlag .
- Benadada , Y. and Ferland , J.A. 1988 . Partial linearization for generalized fractional programming . Z. Oper. Res , 32 : 101 – 106 .
- Bernard , J.C. and Ferland , J.A. 1989 . Convergence of interval-type algorithms for generalized fractional programming . Math. Prog , 43 : 349 – 363 .
- Borde , J. and Crouzeix , J.P. 1987 . Convergence of a Dinkelbach-type algorithm in generalized fractional programming . Z. Oper. Res , 31 : 31 – 54 .
- Bracken , I. and McGill , J.T. 1973 . Mathematical prosrams with optimization problems in the constraints . Oper. Res , 21 : 37 – 44 .
- Bracken , J. and McGill , J.T. 1974 . Defense applications of mathematical programs with optimization in the constraints . Oper. Res , 22 : 1086 – 1096 .
- Chandra , S. , Craven , B.D. and Mond , B. 1986 . Generalized fractional programming: A ratio game approach . J.Austra1. Math. Soc. (Series B) , 28 : 170 – 180 .
- Charnes , A. and Cooper , W.W. 1977 . Goal programming and multiobjective optimization. part I . Europeirn J . Oper. Res , 1 : 39 – 54 .
- Clarke , F.H. 1983 . Optimization uud Nonsmooth Analysis , New York : Wiley .
- Craven , B.D. 1988 . Fractional Programming , Berlin : Heldermann Verlag .
- Craven , B.D. and Mond , B. 1976 . “ Lagrangean conditions for quasidifferentiable optimization ” . In Survey of Mathematical Programming , Edited by: Prékopa , A. Vol. 1 , 177 – 192 . Amsterdam : North-Holland .
- Craven , B.D. and Mond , B. 1983 . On Maximizing a ratio of optimization problems . Cahiers Centre Etudes Rech. Opér , 25 : 29 – 34 .
- Crouzeix , J.P. 1981 . “ A duality framework in quasiconvex programming ” . In Generalized Concatlity in Optimization and Economics , Edited by: Schaible , S. and Ziemba , W.T. 207 – 225 . New York : Academic Press .
- Crouzeix , J.P. , Ferland , J.A. and Schaible , S. 1983 . Duality in generalized linear fractional programming . Math. Prog , 27 : 342 – 354 .
- Crouzeix , J.P. , Ferland , J.A. and Schaible , S. 1985 . An algorithm for generalizedfractional programs . J. Optim. Theory Appl , 47 : 35 – 49 .
- Crouzeix , J.P. , Ferland , J.A. and Schaible , S. 1986 . A note on an algorithm for generalized fractional programs . J. Optim. Theory Appl , 59 : 183 – 187 .
- Demyanov , V.F. and Malozemov , V.N. 1974 . Introduction to Minimax , New York : Wiley .
- Demyanov V. F. Malozemov V. N. Introduction to Minimax Wiley New York 1974
- Ferland , J.A. and Potvin , J.Y. 1985 . Generalized fractional programming: Algorithms and numerical experimentation . European J. Oper. Res , 20 : 92 – 101 .
- Flachs , J. 1982 . Global saddlepoint duality for quasiconcave programs, II . Math. Prog , 24 : 326 – 345 .
- Flachs , J. 1985 . Generalized Cheney-Loeb-Dinkelbach-type algorithms . Math. Oper. Res , 10 : 674 – 687 .
- Ishizuka , Y. 1988 . Optimality conditions for quasidifferentiable programs with application to two level optimization . SIAM J. Control Optim , 26 : 1388 – 1398 .
- Jagannathan , R. 1985 . An algorithm for a class of nonconvex programming problems with nonlinear fractional objectives . Management Sci , 31 : 847 – 851 .
- Jagannathan , R. and Schaible , S. 1983 . Duality in generalized fractional programming via Farkas lemma . J. Optim. Theory Appl , 41 : 417 – 424 .
- Jeyakumar , V. 1986 . On subgradient duality with strong and weak convex functions . J. Austral. Math.Soc. (Series A) , 40 : 143 – 152 .
- Kornbluth , J.S.H. 1973 . A survey of goal programming . Omega , 1 : 193 – 205 .
- Passy , U. and Keslassy , A. 1983 . Duality for a class of quasiconvex programs . J. Optim. Theory Appl , 40 : 515 – 536 .
- Pshenichnyi , B.N. 1971 . Necessary Conditions for an Optimum , New York : Marcel Dekker .
- Schaible , S. 1982 . Bibliography in fractional programming . Z. Oper. Res , 26 : 211 – 241 .
- Scott , C.H. and Jefferson , T.R. 1989 . Conjugate duality in generalized fractional programming . J. Optim. Theory Appl , 60 : 475 – 783 .
- Shimizu , K. , Aiyoshi , E. and Katayama , R. 1983 . Generalized Farkas' theorem and optimization of infinitely constrained problems . J. Optim. Theory Appl , 40 : 451 – 462 .
- Shimizu , K. and Ishizuka , Y. 1985 . Optimality conditions and algorithms for parameter design problems with two-level structure . IEEE Trans. Automat. Control , 30 : 986 – 993 . AC
- Singh , C. and Rucda , N. 1990 . Generalized fractional programming: Optimality and duality theory . J. Optim. Theory Appl , 66 : 149 – 159 .
- Von Neumann , J. 1945 . A model of general economic equilibrium . Reo. Econ. Studies , 13 : 1 – 9 .
- Watson , G.A. 1978 . A class of programming problems whose objective function contains a norm . J. Approx. Theory , 23 : 401 – 411 .
- Xu , Z.K. 1988 . Saddle-point type optimality criteria for generalized fractional programming . J. Optim. Theory Appl , 57 : 189 – 196 .
- Zalmai , G.J. 1989 . A transposition theorem with applications to constrained optimal control problems . Optimization , 20 : 265 – 279 .
- Zalmai , G.J. 1989 . Optimality conditions and duality for constrained measurable subset selection problems with minmax objective functions . Optimization , 20 : 377 – 395 .
- Zalmai , G.J. 1990 . Duality for generalized fractional programs involving n-set functions . J. Math. Anul. Appl , 149 : 339 – 350 .
- Zalmai , G.J. 1990 . Optimality conditions and duality for a class of continuous-time generalized fractional programming problems . J. Math. Anal. Appl , 153 : 356 – 371 .
- Zalmai G. J. A class of generalized fractional optimal control problems containing arbitrary norms Submitted for publication
- Zalmai G. J. Parameter-free duality models for a class of generalized fractional optimal controlproblems containing arbitrary norms Submitted for publication
- Zalmai , G.J. 1994 . Optimality conditions and duality models for a class of nonsmooth constrained fractional variational problems . Optimization , 30 : 15 – 51 .