Parametric duality on minimax programming involving generalized convexity in complex space

In this paper we employ generalized convexity of complex functions to establish several sufficient optimality conditions for minimax programming in complex spaces. Using such criteria, we constitute a parametrical dual, and establish the weak, strong, and strict converse duality theorems in the framework.

[1]  S. Schaible,et al.  Complex Fractional Programming and the Charnes-Cooper Transformation , 2005 .

[2]  Jen-Chwan Liu,et al.  Optimality and duality for complex nondifferentiable fractional programming , 1997 .

[3]  I. Smart,et al.  Complex nonlinear programming: Duality with invexity and equivalent real programs , 1991 .

[4]  A duality theorem for a special class of programming problems in complex space , 1975 .

[5]  B. Mond,et al.  Generalized convexity and duality for complex programming problems , 1984 .

[6]  C. Das,et al.  Nonlinear Complex Programming with Nonlinear Constraints , 1977 .

[7]  H. Lai,et al.  Complex Fractional Programming Involving Generalized Quasi/Pseudo Convex Functions , 2002 .

[8]  B. Craven,et al.  A class of nondifferentiable complex programming problems , 1975 .

[9]  H. Lai,et al.  OPTIMALITY CONDITIONS FOR MINIMAX PROGRAMMING OF ANALYTIC FUNCTIONS , 2004 .

[10]  Davinder Bhatia,et al.  Nonlinear programming in complex space , 1969 .

[11]  O. Ferrero.  On nonlinear programming in complex spaces , 1992 .

[12]  N. Levinson,et al.  Linear programming in complex space , 1966 .

[13]  M. A. Hanson,et al.  Duality for nonlinear programming in complex space , 1969 .

[14]  R. Abrams,et al.  Nonlinear programming in complex space: Sufficient conditions and duality , 1972 .

[15]  T. R. Gulati.  On Nonlinear Nondifferentiable Complex Programming Problems , 1982 .

[16]  D. Bhatia,et al.  Duality for a class of nondifferentiable mathematical programming problems in complex space , 1984 .

[17]  P. Saxena,et al.  Nondifferentiable Fractional Programming in Complex Space , 1984 .

[18]  W. Schmitendorf.  Necessary conditions and sufficient conditions for static minmax problems , 1977 .

[19]  Adi Ben-Israel,et al.  Nonlinear Programming in Complex Space: Necessary Conditions , 1971 .

[20]  B. Craven,et al.  On duality in complex linear programming , 1973, Journal of the Australian Mathematical Society.