Optimality conditions and duality in multiple objective programming involving semilocally convex and related functions

References

• Bector , C.R. , Bector , M.K. and Klassen , J.E. 1977 . Duality for a nonlinear programming problem . Utilitas Math , 11 : 87 – 89 .
   Google Scholar
• Ben-Israel , A. and Mond , B. 1986 . What is invexity? . J. Austral. Math. Soc , 28 : 1 – 9 . Ser.B
   Web of Science ®Google Scholar
• Bitran , G. 1981 . Duality in nonlinear multiple criteria optimization problems . J. Optim. Theory Appl , 35 : 509 – 515 .
   Google Scholar
• Cambini , A. and Martein , L. 1993 . “ An approach to optimality conditions in vector and scalar optimization ” . In Mathematical Modelling in Economics , Edited by: Diewert , Spremann and Stehling . Springer Verlag .
   Google Scholar
• Cambini , A. and Martein , L. 1994 . “ Gerenalized concavity and optimality conditions in vector and scalar optimization in Generalized Convexity ” . Vol. 405 , Springer Verlag . Lecture Notes in Economics and Mathematical Systems
   Google Scholar
• Corley , B.D. 1981 . Duality theory for maximization with respect to cones . J. Math. Anal. Appl , 84 : 560 – 568 .
   Web of Science ®Google Scholar
• Craven , B.D. 1980 . Strong vector minimization and duality . Z. Angew. Math. Mech , 60 : 1 – 5 .
   Web of Science ®Google Scholar
• Craven , B.D. 1986 . On quasidifferentiable optimization . J. Austral. Math. Soc , 41 : 64 – 78 . Series A
   Web of Science ®Google Scholar
• Elster , K.H. and Nehse , R. 1980 . “ Optimality conditions for some nonconvex problems ” . New York : Springer-Verlag .
   Google Scholar
• Ewing , C.M. 1977 . Sufficient conditions for global minima of suitable convex functions from variational and control theory . SIAM Rev , 19 ( 2 ) : 202 – 220 .
   Web of Science ®Google Scholar
• Geoffrion , A.M. 1968 . Proper efficiency and the theory of vector maximization . J. Math. Anal., Appl , 22 ( 2 ) : 618 – 630 .
   Google Scholar
• Hanson , M.A. and Mond , B. 1987 . Convex transformabile programming problems and invexity . J. Inform. Oatim. Sci , 8 ( 2 ) : 179 – 189 .
   Google Scholar
• Hayashi , M. and Komiya , H. 1980 . Perfect duality for convexlike programs . J. Optim. Theory Appl , 38 ( 2 ) : 179 – 189 .
   Google Scholar
• Heal , G. 1984 . Equivalence of saddle-points and optima for non-concave programs . Adcan. in Appl., Math , 5 ( 2 ) : 398 – 415 .
   Google Scholar
• Ivanov , E.H. and Nehse , R. 1985 . Some results on dual vector optimization problems . Math. Oper. Statist. Ser. Optim , 16 ( 2 ) : 505 – 517 .
   Google Scholar
• Jeyakumar , V. 1985 . Convexlike alternative theorems and mathematical programming . Optimization , 16 ( 2 ) : 643 – 652 .
   Google Scholar
• Jeyakumar , V. 1988 . Equivalence of saddle-points and optima, and duality for a class of nonsmooth non-convex problems . J. Math. Anal. Appl , 130 ( 2 ) : 334 – 343 .
   Google Scholar
• Jeyakumar , V. 1991 . Composite nonsmooth programming with Gateaux differentiability . SIAM Journal on Optimization , 1 ( 2 ) : 30 – 41 .
   Google Scholar
• Jeyakumar , V. and Mond , B. 1992 . On generalized convex mathematical programming . J. Austral. Math. Sac , 34 ( 2 ) : 43 – 53 . Ser B
   Google Scholar
• Jeyakumar , V. and Yang , X.Q. 1993 . Convex composite multi–objective nonsmooth programming . Mathematical Programming , 59 ( 2 ) : 325 – 343 .
   Google Scholar
• Kaul , R.N. and Kaur , Surjeet. 1982 . Generalizations of convex and related functions . European Journal of Operational Research , 9 ( 2 ) : 369 – 377 .
   Web of Science ®Google Scholar
• Kaul , R.N. and Kaur , Surjeet. 1982 . Sufficient optimality conditions using generalized convex functions . Opsearch , 19 ( 4 ) : 212 – 224 .
   Google Scholar
• Kaul , R.N. and Kaur , Surjeet. 1984 . “ Generalized convex functions-properties, optimality and duality ” . California : Stanford University . Technical Report SOL, 84-4
   Google Scholar
• Mahajanm , D.G. and Vartak , M.N. 1977 . Generalizations of some duality theorems in nonlinear programming . Mathematical Programming , 12 : 293 – 317 .
   Google Scholar
• Mangasarian , O.L. 1969 . “ Nonlinear Programming ” . New York : McGraw-Hill .
   Google Scholar
• Mond , B. and Weir , T. 1981 . “ Generalized concavity and duality ” . In Generalized Concavity in Optimization and Economics , Edited by: Schaible , S. and Ziemba , W.T. 263 – 280 . New York : Academic Press .
   Google Scholar
• Singh , C. 1988 . Duality theory in multiobjective differentiable programming . J. Inform. Optim. Sci , 9 : 231 – 240 .
   Google Scholar
• Suneja , S.K. and Gupta , Sudha. 1993 . Duality in nonlinear programming involving semilocally convex and related functions . Optimization , 28 : 17 – 29 .
   Google Scholar
• Tanino , T. and Sawaragi , Y. 1979 . Duality in multiobjective programming . J. Optim. Theory Appl , 27 : 509 – 529 .
   Web of Science ®Google Scholar
• Wolfe , P. 1961 . Duality theorems for nonlinear programming . Quart. Appl. Math , 19 : 239 – 244 .
   Google Scholar
• Weir , T. 1987 . Proper efficiency and duality for vector valued optimization problems . J. Austral. Math. Soc , 43 : 21 – 34 . Series A
   Web of Science ®Google Scholar
• Weir , T. and Mond , B. 1988 . Pre-invex functions in multiple objective optimization . J. Math. Anal. Appl , 136 : 29 – 38 .
   Web of Science ®Google Scholar
• Weir , T. and Mond , B. 1989 . Generalized convexity and duality in multiple objective programming . Bull. Austral. Math. Soc , 39 : 287 – 299 .
   Web of Science ®Google Scholar
• White , D.G. 1985 . Vector maximization and Lagrange multipliers . Math. Programming , 31 : 192 – 205 .
   Web of Science ®Google Scholar