In this paper, a pair of Mond-Weir type higher-order symmetric dual programs over arbitrary cones is formulated. The appropriate duality theorems, such as weak duality theorem, strong duality theorem and converse dual...In this paper, a pair of Mond-Weir type higher-order symmetric dual programs over arbitrary cones is formulated. The appropriate duality theorems, such as weak duality theorem, strong duality theorem and converse duality theorem, are established under higher-order （strongly） cone pseudoinvexity assumptions.展开更多
In this paper,a new mixed-type higher-order symmetric duality in scalar-objective programming is formulated.In the literature we have results either Wolfe or Mond–Weir-type dual or separately,while in this we have co...In this paper,a new mixed-type higher-order symmetric duality in scalar-objective programming is formulated.In the literature we have results either Wolfe or Mond–Weir-type dual or separately,while in this we have combined those results over one model.The weak,strong and converse duality theorems are proved for these programs underη-invexity/η-pseudoinvexity assumptions.Self-duality is also discussed.Our results generalize some existing dual formulations which were discussed by Agarwal et al.(Generalized second-order mixed symmetric duality in nondifferentiable mathematical programming.Abstr.Appl.Anal.2011.https://doi.org/10.1155/2011/103597),Chen(Higher-order symmetric duality in nonlinear nondifferentiable programs),Gulati and Gupta(Wolfe type second order symmetric duality in nondifferentiable programming.J.Math.Anal.Appl.310,247–253,2005,Higher order nondifferentiable symmetric duality with generalized F-convexity.J.Math.Anal.Appl.329,229–237,2007),Gulati and Verma(Nondifferentiable higher order symmetric duality under invexity/generalized invexity.Filomat 28(8),1661–1674,2014),Hou andYang(On second-order symmetric duality in nondifferentiable programming.J Math Anal Appl.255,488–491,2001),Verma and Gulati(Higher order symmetric duality using generalized invexity.In:Proceeding of 3rd International Conference on Operations Research and Statistics(ORS).2013.https://doi.org/10.5176/2251-1938_ORS13.16,Wolfe type higher order symmetric duality under invexity.J Appl Math Inform.32,153–159,2014).展开更多
In this paper,we point out some deficiencies in a recent paper(Lee and Kim in J.Nonlinear Convex Anal.13:599–614,2012),and we establish strong duality and converse duality theorems for two types of nondifferentiable...In this paper,we point out some deficiencies in a recent paper(Lee and Kim in J.Nonlinear Convex Anal.13:599–614,2012),and we establish strong duality and converse duality theorems for two types of nondifferentiable higher-order symmetric duals multiobjective programming involving cones.展开更多
Convexity and generalized convexity play important roles in optimization theory. With the development of programming problem, there has been a growing interest in the higher-order dual problem and a lot of related gen...Convexity and generalized convexity play important roles in optimization theory. With the development of programming problem, there has been a growing interest in the higher-order dual problem and a lot of related generalized convexities are given. In this paper, we give the convexity of (F, α ,p ,d ,b , φ )β vector-pseudo- quasi-Type I and formulate a higher-order duality for minimax fractional type programming involving symmetric matrices, and give the weak, strong and strict converse duality theorems under the condition of higher-order (F, α ,p ,d ,b , φ )β vector-pseudoquasi-Type I.展开更多
In this paper,we emphasize on a nondifferentiable minimax fractional programming(NMFP)problem and obtain appropriate duality results for higher-order dual model under higher-order B-(p,r)-invex functions.We provide a ...In this paper,we emphasize on a nondifferentiable minimax fractional programming(NMFP)problem and obtain appropriate duality results for higher-order dual model under higher-order B-(p,r)-invex functions.We provide a nontrivial illustration of a function which belongs to the class of higher-order B-(p,r)-invex but not in the class of second-order B-(p,r)-invex functions already existing in literature.An example of finding a minimax solution of NMFP problem by using higher-order B-(p,r)-invex functions has also been given.Various known results are discussed as particular cases.展开更多
The purpose of this paper is to introduce second order (K, F)-pseudoconvex and second order strongly (K, F)- pseudoconvex functions which are a generalization of cone-pseudoconvex and strongly cone-pseudoconvex functi...The purpose of this paper is to introduce second order (K, F)-pseudoconvex and second order strongly (K, F)- pseudoconvex functions which are a generalization of cone-pseudoconvex and strongly cone-pseudoconvex functions. A pair of second order symmetric dual multiobjective nonlinear programs is formulated by using the considered functions. Furthermore, the weak, strong and converse duality theorems for this pair are established. Finally, a self duality theorem is given.展开更多
A certain constrained dynamic game is shown to be equivalent to a pair of symmetric dual variational problems which have more general formulation than those already existing in the literature. Various duality results ...A certain constrained dynamic game is shown to be equivalent to a pair of symmetric dual variational problems which have more general formulation than those already existing in the literature. Various duality results are proved under convexity and generalized convexity assumptions on the appropriate functionals. The dynamic game is also viewed as equivalent to a pair of dual variational problems without the condition of fixed points. It is also indicated that the equivalent formulation of a pair of symmetric dual variational problems as dynamic generalization of those had been already studied in the literature. In essence, the purpose of the research is to establish that the solution of variational problems yields the solution of the dynamic game.展开更多
On bounded symmetric domain Ω of C^n, we investigate the properties of functions in weighted Bergman spaces A^P（Ω,dvs） for 0 〈 p ≤ ＋∞ and -1 〈 s 〈 4-∞. Based on the estimate of Bergman kernel, we obtain som...On bounded symmetric domain Ω of C^n, we investigate the properties of functions in weighted Bergman spaces A^P（Ω,dvs） for 0 〈 p ≤ ＋∞ and -1 〈 s 〈 4-∞. Based on the estimate of Bergman kernel, we obtain some characterizations of functions in A^P（Ω, dvs） in terms of a class of linear operators D^αB. Making use of these characterizations, we extend A^P（Ω,dvs） to the weighted Bergman spaces Aα^p,B（Ω,dvs） in a very natural way for 1 〈 p 〈 4-∞ and any real number s, that is, -∞ 〈 s 〈 ＋∞. This unified treatment covers some classical Bergman spaces, Besov spaces and Bloch spaces. Meanwhile, the boundedness of Bergman projection operators on Aα^P,β（Ω, dvs） and the dual of Aα^P,B（Ω, dvs） are given.展开更多
In this paper, we first formulate a second-order multiobjective symmetric primal-dual pair over arbitrary cones by introducing two different functions f ： R^n × R^m → Rk and g ： R^n × R^m → R^l in each k...In this paper, we first formulate a second-order multiobjective symmetric primal-dual pair over arbitrary cones by introducing two different functions f ： R^n × R^m → Rk and g ： R^n × R^m → R^l in each k-objectives as well as l-constraints. Further, appropriate duality relations are established under second-order（F, α, ρ, d）-convexity assumptions. A nontrivial example which is second-order（F, α, ρ, d）-convex but not secondorder convex/F-convex is also illustrated. Moreover, a second-order minimax mixed integer dual programs is formulated and a duality theorem is established using second-order（F, α, ρ, d）-convexity assumptions. A self duality theorem is also obtained by assuming the functions involved to be skew-symmetric.展开更多
A pair of symmetric duals for a class of nondifferentiable multiobjective fractional programmings is formulated, and appropriate duality theorems are established.
The notion of higher-order B-type I functional is introduced in this paper.This notion is utilized to study optimality and duality for multiobjective semi-infinite variational problem in which the index set of inequal...The notion of higher-order B-type I functional is introduced in this paper.This notion is utilized to study optimality and duality for multiobjective semi-infinite variational problem in which the index set of inequality constraints is an infinite set.The concept of efficiency is used as a tool for optimization.Mond–Weir type of dual is proposed for which weak,strong,and strict converse duality theorems are proved to relate efficient solutions of primal and dual problems.展开更多
基金Supported by the National Natural Science Foundation of China(No.11431004,11271391 and 11201511)the Natural Science Foundation of Chongqing(CSTC2014pt-sy00001,CSTC2015jcyj A00005)the Education Committee Project Research Foundation of Chongqing(KJ1500309,KJ1400519)
文摘In this paper, a pair of Mond-Weir type higher-order symmetric dual programs over arbitrary cones is formulated. The appropriate duality theorems, such as weak duality theorem, strong duality theorem and converse duality theorem, are established under higher-order （strongly） cone pseudoinvexity assumptions.
基金The research of Khushboo Verma was supported by the Department of Atomic Energy,Govt.of India,the NBHM Post-Doctoral Fellowship Program(No.2/40(31)/2015/RD-II/9474).
文摘In this paper,a new mixed-type higher-order symmetric duality in scalar-objective programming is formulated.In the literature we have results either Wolfe or Mond–Weir-type dual or separately,while in this we have combined those results over one model.The weak,strong and converse duality theorems are proved for these programs underη-invexity/η-pseudoinvexity assumptions.Self-duality is also discussed.Our results generalize some existing dual formulations which were discussed by Agarwal et al.(Generalized second-order mixed symmetric duality in nondifferentiable mathematical programming.Abstr.Appl.Anal.2011.https://doi.org/10.1155/2011/103597),Chen(Higher-order symmetric duality in nonlinear nondifferentiable programs),Gulati and Gupta(Wolfe type second order symmetric duality in nondifferentiable programming.J.Math.Anal.Appl.310,247–253,2005,Higher order nondifferentiable symmetric duality with generalized F-convexity.J.Math.Anal.Appl.329,229–237,2007),Gulati and Verma(Nondifferentiable higher order symmetric duality under invexity/generalized invexity.Filomat 28(8),1661–1674,2014),Hou andYang(On second-order symmetric duality in nondifferentiable programming.J Math Anal Appl.255,488–491,2001),Verma and Gulati(Higher order symmetric duality using generalized invexity.In:Proceeding of 3rd International Conference on Operations Research and Statistics(ORS).2013.https://doi.org/10.5176/2251-1938_ORS13.16,Wolfe type higher order symmetric duality under invexity.J Appl Math Inform.32,153–159,2014).
基金This work was partially supported by the National Natural Science Foundation of China(Nos.11271391 and 10831009)d the Natural Science Foundation of Chongqing(CSTC,No.2011BA0030).
文摘In this paper,we point out some deficiencies in a recent paper(Lee and Kim in J.Nonlinear Convex Anal.13:599–614,2012),and we establish strong duality and converse duality theorems for two types of nondifferentiable higher-order symmetric duals multiobjective programming involving cones.
文摘Convexity and generalized convexity play important roles in optimization theory. With the development of programming problem, there has been a growing interest in the higher-order dual problem and a lot of related generalized convexities are given. In this paper, we give the convexity of (F, α ,p ,d ,b , φ )β vector-pseudo- quasi-Type I and formulate a higher-order duality for minimax fractional type programming involving symmetric matrices, and give the weak, strong and strict converse duality theorems under the condition of higher-order (F, α ,p ,d ,b , φ )β vector-pseudoquasi-Type I.
文摘In this paper,we emphasize on a nondifferentiable minimax fractional programming(NMFP)problem and obtain appropriate duality results for higher-order dual model under higher-order B-(p,r)-invex functions.We provide a nontrivial illustration of a function which belongs to the class of higher-order B-(p,r)-invex but not in the class of second-order B-(p,r)-invex functions already existing in literature.An example of finding a minimax solution of NMFP problem by using higher-order B-(p,r)-invex functions has also been given.Various known results are discussed as particular cases.
文摘The purpose of this paper is to introduce second order (K, F)-pseudoconvex and second order strongly (K, F)- pseudoconvex functions which are a generalization of cone-pseudoconvex and strongly cone-pseudoconvex functions. A pair of second order symmetric dual multiobjective nonlinear programs is formulated by using the considered functions. Furthermore, the weak, strong and converse duality theorems for this pair are established. Finally, a self duality theorem is given.
文摘A certain constrained dynamic game is shown to be equivalent to a pair of symmetric dual variational problems which have more general formulation than those already existing in the literature. Various duality results are proved under convexity and generalized convexity assumptions on the appropriate functionals. The dynamic game is also viewed as equivalent to a pair of dual variational problems without the condition of fixed points. It is also indicated that the equivalent formulation of a pair of symmetric dual variational problems as dynamic generalization of those had been already studied in the literature. In essence, the purpose of the research is to establish that the solution of variational problems yields the solution of the dynamic game.
基金the NNSF of China(10571164)the SRFDP of Higher Education(20050358052)
文摘On bounded symmetric domain Ω of C^n, we investigate the properties of functions in weighted Bergman spaces A^P（Ω,dvs） for 0 〈 p ≤ ＋∞ and -1 〈 s 〈 4-∞. Based on the estimate of Bergman kernel, we obtain some characterizations of functions in A^P（Ω, dvs） in terms of a class of linear operators D^αB. Making use of these characterizations, we extend A^P（Ω,dvs） to the weighted Bergman spaces Aα^p,B（Ω,dvs） in a very natural way for 1 〈 p 〈 4-∞ and any real number s, that is, -∞ 〈 s 〈 ＋∞. This unified treatment covers some classical Bergman spaces, Besov spaces and Bloch spaces. Meanwhile, the boundedness of Bergman projection operators on Aα^P,β（Ω, dvs） and the dual of Aα^P,B（Ω, dvs） are given.
基金Department of Mathematics,Indian Institute of Technology Patna,Patna 800 013,India
文摘In this paper, we first formulate a second-order multiobjective symmetric primal-dual pair over arbitrary cones by introducing two different functions f ： R^n × R^m → Rk and g ： R^n × R^m → R^l in each k-objectives as well as l-constraints. Further, appropriate duality relations are established under second-order（F, α, ρ, d）-convexity assumptions. A nontrivial example which is second-order（F, α, ρ, d）-convex but not secondorder convex/F-convex is also illustrated. Moreover, a second-order minimax mixed integer dual programs is formulated and a duality theorem is established using second-order（F, α, ρ, d）-convexity assumptions. A self duality theorem is also obtained by assuming the functions involved to be skew-symmetric.
文摘A pair of symmetric duals for a class of nondifferentiable multiobjective fractional programmings is formulated, and appropriate duality theorems are established.
基金Jyoti was supported by University Grant Commission Non-NET research fellowship,India(No.Schs/Non-NET/139/Ext-142/2015-16/1931).
文摘The notion of higher-order B-type I functional is introduced in this paper.This notion is utilized to study optimality and duality for multiobjective semi-infinite variational problem in which the index set of inequality constraints is an infinite set.The concept of efficiency is used as a tool for optimization.Mond–Weir type of dual is proposed for which weak,strong,and strict converse duality theorems are proved to relate efficient solutions of primal and dual problems.
