Optimality Conditions And Duality Of H-(p,r)-η Invariant Convex Programming Problems

Multi-objective optimization,as an important branch of optimization field,focuses on the simultaneous optimization of multiple numerical objectives under certain conditions.Multi-objective programming theory involves a series of disciplines such as convex analysis,stochastic analysis and functional analysis.In many practical problems,it is difficult to judge whether a scheme is good or bad with one index,but it needs to be compared with multiple objectives,which are sometimes uncoordinated or even contradictory.Therefore,the research on multi-objective optimization has very important practical significance.Convex function theory is widely used in mathematical programming,cybernetics and complex analysis.At present,various kinds of multi-objective programming under different generalized convexity assumptions have rich achievements in optimality and duality theory,and some scholars continue to conduct in-depth research on multi-objective optimization.A new class of invexity functions is defined in this thesis,the optimality conditions and duality results of multi-objective programming and multi-objective fractional programming under the assumption of generalized convexity is researched.The main contents are as follows:1.A new class of H-(p,r)-η invariant convex functions is defined.Under the assumption of generalized convexity,the optimality of solutions for a class of multi-objective programming problems is studied,and some sufficient conditions for optimality of solutions are obtained.Wolfe-type duality and Mond-Weir-type duality models of this kind of multi-objective programming are established,and the corresponding weak duality,strong duality and strict inverse duality theorems are proved.2.The Hb-(p,r)-η invariant convex function is generalized,and under the assumption of generalized convexity,the optimality sufficient condition that the solution of multi-objective fractional programming is weakly efficient is proved.Wolfe-type duality and Mond-Weir-type duality models for multi-objective fractional programming are established,and the corresponding weak duality and strong duality theorems are prove.In this thesis,a class of invariant convex functions is redefined,and some optimality conditions and duality conclusions are obtained,which enriches the existing convex function theory,enriches the related results of convex functions and multi-objective programming,and has certain research significance in theory.