ABSTRACT
For many problems encountered in economics and engineering the notion of convexity no longer suffices. To meet this demand and the aim of extending the validity of sufficiency of the Karush-Kuhn-Tucker conditions for differentiable mathematical programming problems, the notion of invexity was introduced by Hanson [99] and named by Craven [53]. Hanson [99] introduced a new class of functions, which generalizes both the classes of invex and pseudoconvex functions, called η-pseudoconvex functions by Kaul and Kaur [137] and pseudoinvex functions by Craven [52]. Ben-Israel and Mond [21] have characterized that a real-valued function f is invex if and only if every stationary point is a global minimizer and pointed out that the classes of pseudoinvex functions and invex functions coincide. In 1988, Weir and Mond [283] introduced a new class of functions known as preinvex functions. Differentiable preinvex functions are invex with respect to the same vector function η, however, the converse holds true only if the vector function η satisfies condition C due to Mohan and Neogy [205]. Rueda [240] studied the properties of functions f , for which f and −f are both pseudoinvex with respect to same vector functions η. Later, Ansari et al. [5] called such functions ηpseudolinear functions and derived several characterizations for the solution set of η-pseudolinear programming problems. Giorgi and Rueda [91] have derived the optimality conditions for a vector optimization problem involving η-pseudolinear functions and established that every efficient solution is properly efficient under certain boundedness conditions. Zhao and Yang [299] have used the linear scalarization method to establish the equivalence between efficiency and proper efficiency of a multiobjective optimization problem using the properties of η-pseudolinear functions.
