In this papert the theory of major efficiency for multiobjective programmingis established.The major-efficient solutions and weakly major-efficient solutions of multiobjective programming given here are Pareto efficie...In this papert the theory of major efficiency for multiobjective programmingis established.The major-efficient solutions and weakly major-efficient solutions of multiobjective programming given here are Pareto efficient solutions of the same multiobjectiveprogramming problem, but the converse is not true. In a ceratin sense , these solutionsare in fact better than any other Pareto efficient solutions. Some basic theorems whichcharacterize major-efficient solutions and weakly major-efficient solutions of multiobjective programming are stated and proved. Furthermore,the existence and some geometricproperties of these solutions are studied.展开更多
New classes of functions namely (V, ρ)_(h,φ)-type I, quasi (V, ρ)_(h,φ)-type I and pseudo (V, ρ)_(h,φ)-type I functions are defined for multiobjective programming problem by using BenTal's generalized algebr...New classes of functions namely (V, ρ)_(h,φ)-type I, quasi (V, ρ)_(h,φ)-type I and pseudo (V, ρ)_(h,φ)-type I functions are defined for multiobjective programming problem by using BenTal's generalized algebraic operation. The examples of (V, ρ)_(h,φ)-type I functions are given. The sufficient optimality conditions are obtained for multi-objective programming problem involving above new generalized convexity.展开更多
As we know, the Pareto efficient (optimal) solution or in other words, thenoninferior solution, is a basic concept in multiobjective programming. In thesense of this kind of solution, much theoretical and application ...As we know, the Pareto efficient (optimal) solution or in other words, thenoninferior solution, is a basic concept in multiobjective programming. In thesense of this kind of solution, much theoretical and application work has been doneon solutions in multiobjective programming since the 1950s. However, because thePareto efficient solution is only a solution with respect to a vector objective beingnoinnferior, as for a given multiobjective programming problem, its set is large whenthe number of objectives is great. This is an inevitable flaw caused by definingPareto efficient solution with the partial order induced by a positive cone. Yu intro-duced the nondominated solution on the basis of a general convex cone or展开更多
In this short note.we discuss the relations between linear bilevel programming and linear bicriteria programming.A counter example is comtructed to illustrate the the main result in Wen and Hsu[3]is not correct.A suff...In this short note.we discuss the relations between linear bilevel programming and linear bicriteria programming.A counter example is comtructed to illustrate the the main result in Wen and Hsu[3]is not correct.A sufficient condition is also presented to guarantee at least of optimal solution of a linear bilevel programming problem is also an efficient solution of the corresponding bicriteria programming problem.展开更多
In this paper, we investigate the connectedness of G-proper efficient solution set for multiobjective programming problem. It is shown that the G-proper efficient solution set is connected if objective functions are c...In this paper, we investigate the connectedness of G-proper efficient solution set for multiobjective programming problem. It is shown that the G-proper efficient solution set is connected if objective functions are convex. A sufficient condition for the connectedness of G-proper efficient solution set is established when objective functions are strictly quasiconvex.展开更多
In this paper, we introduce the comparison number for one feasible solutioncompared with another. With the help of it the comparison-number method for find-ing the major optimal solutions aud major efficient solutions...In this paper, we introduce the comparison number for one feasible solutioncompared with another. With the help of it the comparison-number method for find-ing the major optimal solutions aud major efficient solutions to discrete multiobjectiveprogramming is given.展开更多
This paper deals with the connectedness of the cone-efficient solution set for vector optimization inlocally convex Hausdorff topological vector spaces.The connectedness of the cone-efficient solution set is provedfor...This paper deals with the connectedness of the cone-efficient solution set for vector optimization inlocally convex Hausdorff topological vector spaces.The connectedness of the cone-efficient solution set is provedfor multiobjective programming defined by a continuous cone-quasiconvex mapping on a compact convex set ofalternatives.The generalized saddle theorem plays a key role in the proof.展开更多
In this papers the Fritz John conditions and Kuhn-Tucker conditions for majoroptimal solutions and major efficient solutions of multiobjective programming are givenand proved.
In this paper, weak strictly convex vector function and weak strictly H\-α convex vector function are introduced. We prove the uniqueness of major efficient solution when the objective function is weak strictly c...In this paper, weak strictly convex vector function and weak strictly H\-α convex vector function are introduced. We prove the uniqueness of major efficient solution when the objective function is weak strictly convex vector function, and the uniqueness of α major efficient solution when the objective function is weak strictly H α convex vector function.展开更多
An energy effi cient resource allocation scheme in timesharing multiuser system with a hybrid energy harvesting transmitter is studied in this paper. Specially, the operation energy of system is supplied by constant e...An energy effi cient resource allocation scheme in timesharing multiuser system with a hybrid energy harvesting transmitter is studied in this paper. Specially, the operation energy of system is supplied by constant energy and energy harvesting, which harvests energy from external environment. Our goal is to maximize the energy effi ciency of timesharing multiuser systems by considering jointly allocation of transmission time and power control in an off-line manner. The original nonconvex objective function is transformed into convex optimization problem via the fractional programming approach. Then, we solve the convex problem by Lagrange dual decomposition method. Simulation results show that the proposed energy efficient resource allocation scheme has a better performance than the scheme which decomposes optimization problem into two parts(power allocation, time allocation) to solve iteratively.展开更多
In this paper, optimality conditions for multiobjective programming problems having V-invex objective and constraint functions are considered. An equivalent multiobjective programming problem is constructed by a modif...In this paper, optimality conditions for multiobjective programming problems having V-invex objective and constraint functions are considered. An equivalent multiobjective programming problem is constructed by a modification of the objective function.Furthermore, a (α, η)-Lagrange function is introduced for a constructed multiobjective programming problem, and a new type of saddle point is introduced. Some results for the new type of saddle point are given.展开更多
文摘In this papert the theory of major efficiency for multiobjective programmingis established.The major-efficient solutions and weakly major-efficient solutions of multiobjective programming given here are Pareto efficient solutions of the same multiobjectiveprogramming problem, but the converse is not true. In a ceratin sense , these solutionsare in fact better than any other Pareto efficient solutions. Some basic theorems whichcharacterize major-efficient solutions and weakly major-efficient solutions of multiobjective programming are stated and proved. Furthermore,the existence and some geometricproperties of these solutions are studied.
基金Supported by the NSF of Shaanxi Provincial Educational Department(06JK152)
文摘New classes of functions namely (V, ρ)_(h,φ)-type I, quasi (V, ρ)_(h,φ)-type I and pseudo (V, ρ)_(h,φ)-type I functions are defined for multiobjective programming problem by using BenTal's generalized algebraic operation. The examples of (V, ρ)_(h,φ)-type I functions are given. The sufficient optimality conditions are obtained for multi-objective programming problem involving above new generalized convexity.
文摘As we know, the Pareto efficient (optimal) solution or in other words, thenoninferior solution, is a basic concept in multiobjective programming. In thesense of this kind of solution, much theoretical and application work has been doneon solutions in multiobjective programming since the 1950s. However, because thePareto efficient solution is only a solution with respect to a vector objective beingnoinnferior, as for a given multiobjective programming problem, its set is large whenthe number of objectives is great. This is an inevitable flaw caused by definingPareto efficient solution with the partial order induced by a positive cone. Yu intro-duced the nondominated solution on the basis of a general convex cone or
文摘In this short note.we discuss the relations between linear bilevel programming and linear bicriteria programming.A counter example is comtructed to illustrate the the main result in Wen and Hsu[3]is not correct.A sufficient condition is also presented to guarantee at least of optimal solution of a linear bilevel programming problem is also an efficient solution of the corresponding bicriteria programming problem.
基金This work is supported by Research Foundation of the Education Departm entof Zhejiang Province(2 0 0 10 2 80 )
文摘In this paper, we investigate the connectedness of G-proper efficient solution set for multiobjective programming problem. It is shown that the G-proper efficient solution set is connected if objective functions are convex. A sufficient condition for the connectedness of G-proper efficient solution set is established when objective functions are strictly quasiconvex.
基金Research supported by the National Natural Science Foundation of China.
文摘In this paper, we introduce the comparison number for one feasible solutioncompared with another. With the help of it the comparison-number method for find-ing the major optimal solutions aud major efficient solutions to discrete multiobjectiveprogramming is given.
基金Supported by the National Natural Science Foundation of China (No.70071026)
文摘This paper deals with the connectedness of the cone-efficient solution set for vector optimization inlocally convex Hausdorff topological vector spaces.The connectedness of the cone-efficient solution set is provedfor multiobjective programming defined by a continuous cone-quasiconvex mapping on a compact convex set ofalternatives.The generalized saddle theorem plays a key role in the proof.
文摘In this papers the Fritz John conditions and Kuhn-Tucker conditions for majoroptimal solutions and major efficient solutions of multiobjective programming are givenand proved.
文摘In this paper, weak strictly convex vector function and weak strictly H\-α convex vector function are introduced. We prove the uniqueness of major efficient solution when the objective function is weak strictly convex vector function, and the uniqueness of α major efficient solution when the objective function is weak strictly H α convex vector function.
基金supported in part by the National Natural Science Foundation of China(61471115)in part by the 2016 Science and Technology Joint Research and Innovation Foundation of Jiangsu Province(BY2016076-13)
文摘An energy effi cient resource allocation scheme in timesharing multiuser system with a hybrid energy harvesting transmitter is studied in this paper. Specially, the operation energy of system is supplied by constant energy and energy harvesting, which harvests energy from external environment. Our goal is to maximize the energy effi ciency of timesharing multiuser systems by considering jointly allocation of transmission time and power control in an off-line manner. The original nonconvex objective function is transformed into convex optimization problem via the fractional programming approach. Then, we solve the convex problem by Lagrange dual decomposition method. Simulation results show that the proposed energy efficient resource allocation scheme has a better performance than the scheme which decomposes optimization problem into two parts(power allocation, time allocation) to solve iteratively.
基金Supported by the National Natural Science Foundation of China(19871009)
文摘In this paper, optimality conditions for multiobjective programming problems having V-invex objective and constraint functions are considered. An equivalent multiobjective programming problem is constructed by a modification of the objective function.Furthermore, a (α, η)-Lagrange function is introduced for a constructed multiobjective programming problem, and a new type of saddle point is introduced. Some results for the new type of saddle point are given.
