ABSTRACT
Convexity plays a central role in optimization theory. To provide a more accurate representation, modelling and solutions of several real world problems, various generalizations of convexity have been introduced. Mangasarian [176] has introduced pseudoconvex and pseudoconcave functions as generalizations of convex and concave functions, respectively. Kortanek and Evans [149] investigated the properties of the functions, which are both pseudoconvex as well as pseudoconcave. Many authors extended the study of this class of functions, which were later termed as pseudolinear functions. Chew and Choo [47] derived first and second order characterizations for differentiable pseudolinear functions. The class of pseudolinear functions includes many important classes of functions, for example, the linear and quadratic fractional functions, which arise in many practical applications (see [34, 246]). Rapcsak [233] characterized the general form of gradient of twice continuously differentiable pseudolinear functions on Riemannian manifolds. Komlosi [147] presented the characterizations of the differentiable pseudolinear functions using a special property of the normalized gradient.
