Proper efficiency and duality for vector valued optimization problems

The duality results of Wolfe for scalar convex programming problems and some of the more recent duality results for scalar nonconvex programming problems are extended to vector valued programs. Weak duality is established using a 'Pareto' type relation between the primal and dual objective functions. 1980 Mathematics subject classification (Amer. Math. Soc): primary 90 C 31; secondary 90 C 30.

[1]  G. R. Bitran,et al.  Duality for nonlinear multiple-criteria optimization problems , 1981 .

[2]  W. Ziemba,et al.  Generalized concavity in optimization and economics , 1981 .

[3]  David G. Luenberger,et al.  Quasi-Convex Programming , 1968 .

[4]  B. Craven Strong Vector Minimization and Duality , 1980 .

[5]  Douglas J. White,et al.  Vector maximisation and lagrange multipliers , 1985, Math. Program..

[6]  Olvi L. Mangasarian,et al.  Minmax and duality in nonlinear programming , 1965 .

[7]  P. Wolfe A duality theorem for non-linear programming , 1961 .

[8]  Josef Stoer,et al.  Duality in nonlinear programming and the minimax theorem , 1963 .

[9]  R. Rockafellar Conjugate Duality and Optimization , 1987 .

[10]  Olvi L. Mangasarian,et al.  Nonlinear Programming , 1969 .

[11]  H. W. Corley,et al.  Duality theory for maximizations with respect to cones , 1981 .

[12]  D. White Concepts of proper efficiency , 1983 .

[13]  S. Sinha A Duality Theorem for Nonlinear Programming , 1966 .

[14]  Y. Sawaragi,et al.  Duality theory in multiobjective programming , 1979 .

[15]  L. Sandgren On convex cones , 1954 .

[16]  Y. Sawaragi,et al.  Conjugate maps and duality in multiobjective optimization , 1980 .

[17]  A. M. Geoffrion Proper efficiency and the theory of vector maximization , 1968 .

[18]  R. Rockafellar 1. Conjugate Duality and Optimization , 1974 .

[19]  R. Nehse,et al.  Some results on dual vector optimization problems 1 , 1985 .

[20]  A. M. Geoffrion Duality in Nonlinear Programming: A Simplified Applications-Oriented Development , 1971 .

[22]  D. G. Mahajan,et al.  Generalization of some duality theorems in nonlinear programming , 1977, Math. Program..