Abstract
This paper deals with the optimality conditions and dual theory of multi-objective programming problems involving generalized convexity. New classes of generalized type-I functions are introduced for arcwise connected functions, and examples are given to show the existence of these functions. By utilizing the new concepts, several sufficient optimality conditions and Mond-Weir type duality results are proposed for non-differentiable multi-objective programming problem.
Highlights
Investigation on sufficiency and duality has been one of the most attraction topics in the theory of multi-objective problems
It is well known that the concept of convexity and its various generalizations play an important role in deriving sufficient optimality conditions and duality results for multi-objective programming problems
The type-I functions were extended to several classes of generalized type-I functions by many researchers, and sufficient optimality criteria and duality results are established for multi-objective programming problems involving these functions
Summary
Investigation on sufficiency and duality has been one of the most attraction topics in the theory of multi-objective problems. The type-I functions were extended to several classes of generalized type-I functions by many researchers, and sufficient optimality criteria and duality results are established for multi-objective programming (vector optimization) problems involving these functions (see [1,2,3,4,5,6,7,8,9,10,11,12]).
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