Duality of Multi-objective Programming

The convexity theory plays an important role in many aspects of mathematical programming. In recent years, in order to relax convexity assumption, various generalized convexity notions have been obtained. One of them is the concept of ) , ( r p B− invexity defined by T.Antczak [1], which extended the class of B − invex functions with respect toη and b and the classes of ) , ( r p invex functions with respect toη [2][3]. He proved some necessary and sufficient conditions for) , ( r p B− invexity and showed the relationships between the defined ) , ( r p B− -invex functions and other classes of invex functions. Later Antczak defined a classes of generalized invex functions[4], that is ) , ( r p B− pseudo-invex functions, strictly ) , ( r p B− pseudo-invex functions, and ) , ( r p B− quasi-invex functions, considered single objective mathe -matical programming problem involving ) , ( r p B− pseudo-invex functions, ) , ( r p B− quasi-invex functions and obtained some sufficient optimality conditions. Qing xing Zhang[5][6]defined B -arcwise connected functions,