Optimality Conditions Of The αk-major Efficient Solutions For Multiobjective Programming Under B-invariant Convexity

There are many options to choose from a complex task. In order to get good results,people always try to follow a certain standard from a number of options available to pick out the best or satisfactory solution. If the problem is only considered one target selection for criteria, people should try to make this goal optimal. However, in practice, people often need to consider of multiple targets.Multi-objective optimization problem is a study of more than one objective function in a given area on the optimization. It applys in program management, financial decision-making, economic planning, engineering design, energy development, military science, health care and other fields.At first,this paper describes the background and present situations of this subject, and then introduces the mathematical model of the multi-objective optimization problem. Then systematically introduces its solution (including solutions and varieties of solution sets) .In addition,this paper Elaborates of a new function that is B - vex function convex convexity and proves some related properties. Optimality condition is an important research direction .In this regard, there are many previous results .But, at certain condions,the research of optimal conditions of research should be promoted better. So,I make use of B -invariant convexity, to prove optimality conditions ofαk- major efficient solutions for multiobjective programming, which extends the results of previous studies.