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Abstract
New two classes of real differentiable functions, called (p, r)-Type I and (p, r)-Type II with respect to η, which represent a generalization of the notion of invexity, are introduced. Some examples of these functions are derived. The sufficient optimality conditions are obtained for a nonlinear programming problem involving (p, r)-Type I functions with respect to η and for an associated Wolfe dual problem in which involved functions are (p, 0)-Type II. It is also shown that the optimization problems possesing the considered notion of invexity need not to be equivalent to the class of optimization problems for which some notion of invexity guarantees that Karush–Kuhn–Tucker necessary conditions for optimality are also sufficient and the sufficiency for optimality in associated Wolfe dual problems.