On generalized convex functions in optimization theory-A survey

Both the theory of optimization and mathematical programming deal with the existence and uniqueness of the optimal solution together with continuous dependence on the problem data. Further they also deal with the concept of convergence of the minimizing sequence to the unique minimum point. These concepts are much used in the development of algorithms and techniques to solve problems in optimization. This kind of study in optimization involves different classes of generalized convex function viz, strongly pseudoconvex, quasiconvex, invex, strongly pseudoinvex, pseudoinvex, quasinvex, B-vex, pseudo B-vex, Quasi B-Vex, B-invex, pseudo B-invex and quasi B-invex. In this paper, the authors study their relations with convex functions and the interrelations between them.