Generalizations of Higher-Order Duality for Multiple Objective Nonlinear Programming under the Generalizations of Type-I Functions

Abstract

In this study, we introduce new generalizations of higher-order type-I functions and higher-order pseudo-convexity type-I functions. The application of the notion of sublinear functionals to these generalizations of higher-order type-I and higher-order pseudo-convexity type-I functions is crucial to our main findings. Furthermore, under these generalizations of the higher-order type-I and higher-order pseudo-convexity type-I functions, we established and studied six new types of higher-order duality models and programs for multiple objective nonlinear programming problems. In addition, we use these generalizations of higher-order type-I functions and higher-order pseudo-convexity type-I functions, to formulate and prove the theorems of weak duality, strong duality, and strict converse duality for these new six types of higher-order model programs.

Keywords

• multiple objective programming
• nonlinear programming
• higher-order duality
• (<i>F</i>,<i>ρ</i>,<i>σ</i>)-type-I functions
• pseudo-convexity functions