Chapter

Generalized Convexity and Related Topics

Volume 583 of the series Lecture Notes in Economics and Mathematical Systems pp 167-176

Mathematical Programming with (Φ, ρ)-invexity

  • Giuseppe CaristiAffiliated withFaculty of Economics, University of Messina
  • , Massimiliano FerraraAffiliated withFaculty of Economics, University of Messina
  • , Anton StefanescuAffiliated withFaculty of Mathematics and Computer Science, University of Bucharest

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Summary

We introduce new invexity-type properties for differentiable functions, generalizing (F, ρ)-convexity. Optimality conditions for nonlinear programming problems are established under such assumptions, extending previously known results. Wolfe and Mond-Weir duals are also considered, and we obtain direct and converse duality theorems.

Key words

Nonlinear programming generalized invexity duality