Duality under novel generalizations of the D-type-I functions for multiple objective nonlinear programming problems

Abstract

In this paper, we provide novel generalizations of the D-type-I functions by relaxing the D-Preinvexity functions using the mean-valued theorem. Under these new generalizations of the D-Preinvexity type-I functions, we also study the optimality solutions for multiple objective nonlinear programming problems. We also establish and illustrate the duality theorems (weak, strong, and converse) for the Wolf-type and Mond-Weir-type for multiple objective nonlinear programming problems using these new generalizations of the D-Preinvexity type-I functions.

Keywords

• Multiple objective programming
• Nonlinear programming
• Duality theorems
• Preinvexity functions
• Type-I functions