Two Classes Of Semi-B-preinvex Functions

Convexity is an important mathematical concept.As a new mathematical branch science,convex analysis came into being in 1960s.Convex sets and convex functions are the fundamental studying contents of convex analysis.Now it is an important. theorical foundation and useful tool of mathematical programming,optimization theory etc.But the limitations of convex function are also obvious.A number of functions about practical problems are nonconvex functions.For the need of solving practical problems.People has generalized the convexity from different point of view.So, studying the generalized forms of convexity and applications in optimization theory are very important and interesting.Chapter 1 acts as the general introduction to the significance and current situation in the study of the invexity.Chapter 2,first,by using semi-B-preinvexity functions,two classes of new generalized convex functions called strictly semi-B-preinvex and semistrictly semi-B-preinvex are defined.It is shown with the aid of some examples that it is real generalization of the semipreinvex and B-vex function.Then,we obtain some basic properties of the two classes of functions.Chapter 3 discuss the applications of the two classes of functions in optimization theory.Then we consider the multiobjective programming problems,in which the objective and the constraint functions are nondifferentiable and differentiable respectively and establish some optimality conditions;consider the multiobjective fractional programming and establish some saddle optimality conditions;establish Wolfe-type duality for multiobjective fractional programming problems and obtain some weak duality,strony duality and strict convexse duality theorems. Chapter 4 comes to a conclusion.In the meanwhile,it put forward some problems for further Study.