Optimality Conditions And Duality Theory For Fraction Optimization Problems Involving Composite Function

In this paper,we study the Optimality condition of general fractional op-timization problem and the fractional optimization problem with composite function.moreover,the Farkas lemma and total duality to obtained between the fractional optimization problem with composite function and its Fenchel-Lagrange duality problem.This paper consists five chapters.In the first chapter,the research background and the main conclusions for general fractional optimization problem and the fractional optimization problem with composite function are introduced.In the second chapter,we provide some notations,conceptions and lemmas.In the third chapter,we study the the Optimality condition of general fractional optimization problem.In the case when the involved functions are not necessarily lower semicontinuous and the sets are not necessarily closed,by using the properties of subdifferentials.some new constraint qualifications are introduced and local/global optimality conditions for the constrained fractional optimization problem are obtained,which extend the corresponding results in the previous paper.In the fourth chapter,we consider the optimality condition of the fraction-al optimization problem with composite function.A series of new constraint qualifications are introduced by using the subdifferential property of the func-tion.By using those qualifications,the optimality condition of the fractional optimization problem with composite function are given.Our results extend the corresponding results in the previous paper.In the five chapter,we consider the Fenchel-Lagrange duality of the frac-tional optimization problem with composite function.A series of new constraint qualifications are introduced by using the subdifferential property of the func-tion.By using those qualifications,the Farkas lemma and total duality to hold between the fractional optimization problem with composite function and its Fenchel-Lagrange dual problem are given.