St. Frunza"3 laid the foundation of-duality theorem for decomposable operators. He proved that if y￡J?(X) is a 2-decomposable operator, then T* is also a 2-decomposable operator. His proof is fundamental, but it...St. Frunza"3 laid the foundation of-duality theorem for decomposable operators. He proved that if y￡J?(X) is a 2-decomposable operator, then T* is also a 2-decomposable operator. His proof is fundamental, but it is rather complicated. Here we give a very simple proof, using Dieudonn^’s duality theorem.Wang Shengwang proved that if T* is a decomposable operator, and F a closed set, then -STJ.^) is weak* closed. In this paper we prove if T* has the single-valued extension property, then xt*(f~) is weak* closed whenever it is closed in the strong topology.展开更多
This paper studies a class of multiobjective generalized fractional programming problems, where the numerators of objective functions are the sum of differentiable function and convex function, while the denominators ...This paper studies a class of multiobjective generalized fractional programming problems, where the numerators of objective functions are the sum of differentiable function and convex function, while the denominators are the difference of differentiable function and convex function. Under the assumption of Calmness Constraint Qualification the Kuhn-Tucker type necessary conditions for efficient solution are given, and the Kuhn-Tucker type sufficient conditions for efficient solution are presented under the assumptions of （F, α, ρ, d）-V-convexity. Subsequently, the optimality conditions for two kinds of duality models are formulated and duality theorems are proved.展开更多
In this paper, we use the concepts of (F, ρ) invexity, (F, ρ) quasiinvexity and (F,ρ) pseudoinvexity etc. to discuss the generalized convex programming min f(x) s.t. g i(x) 0 (i=1,…,m) g j(x)=0 ...In this paper, we use the concepts of (F, ρ) invexity, (F, ρ) quasiinvexity and (F,ρ) pseudoinvexity etc. to discuss the generalized convex programming min f(x) s.t. g i(x) 0 (i=1,…,m) g j(x)=0 (j=1,…, n), x ∈ Xand obtain various duality theorems. Where X is a Frechet space. f,g i(i=1,…, m) and h j(j=1, …, n) are functions from X to R 1.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
A semi-infinite programming problem is a mathematical programming problem with a finite number of variables and infinitely many constraints. Duality theories and generalized convexity concepts are important research t...A semi-infinite programming problem is a mathematical programming problem with a finite number of variables and infinitely many constraints. Duality theories and generalized convexity concepts are important research topics in mathematical programming. In this paper, we discuss a fairly large number of paramet- ric duality results under various generalized （η,ρ）-invexity assumptions for a semi-infinite minmax fractional programming problem.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
In this paper, we present several parametric duality results under various generalized （a,v,p）-V- invexity assumptions for a semiinfinite multiobjective fractional programming problem.
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
This paper studies a dynamic mean-variance portfolio selection problem with random liability in the affine interest rate environment, where the financial market consists of three assets: one risk-free asset, one risky...This paper studies a dynamic mean-variance portfolio selection problem with random liability in the affine interest rate environment, where the financial market consists of three assets: one risk-free asset, one risky asset and one zero-coupon bond. Assume that short rate is driven by affine interest rate model and liability process is described by the drifted Brownian motion, in addition, stock price dynamics is affected by interest rate dynamics. The investors expect to look for an optimal strategy to minimize the variance of the terminal surplus for a given expected terminal surplus. The efficient strategy and the efficient frontier are explicitly obtained by applying dynamic programming principle and Lagrange duality theorem. A numerical example is given to illustrate our results and some economic implications are analyzed.展开更多
基金Supported by the Educational Ministry Science Technique Research Key Foundation of China (108154)the National Natural Science Foundation of China (10871170)
文摘This paper gives a duality theorem for weak L-R smash products, which extends the duality theorem for weak smash products given by Nikshych.
文摘St. Frunza"3 laid the foundation of-duality theorem for decomposable operators. He proved that if y￡J?(X) is a 2-decomposable operator, then T* is also a 2-decomposable operator. His proof is fundamental, but it is rather complicated. Here we give a very simple proof, using Dieudonn^’s duality theorem.Wang Shengwang proved that if T* is a decomposable operator, and F a closed set, then -STJ.^) is weak* closed. In this paper we prove if T* has the single-valued extension property, then xt*(f~) is weak* closed whenever it is closed in the strong topology.
基金Supported by Chongqing Key Lab. of Operations Research and System Engineering
文摘This paper studies a class of multiobjective generalized fractional programming problems, where the numerators of objective functions are the sum of differentiable function and convex function, while the denominators are the difference of differentiable function and convex function. Under the assumption of Calmness Constraint Qualification the Kuhn-Tucker type necessary conditions for efficient solution are given, and the Kuhn-Tucker type sufficient conditions for efficient solution are presented under the assumptions of （F, α, ρ, d）-V-convexity. Subsequently, the optimality conditions for two kinds of duality models are formulated and duality theorems are proved.
文摘In this paper, we use the concepts of (F, ρ) invexity, (F, ρ) quasiinvexity and (F,ρ) pseudoinvexity etc. to discuss the generalized convex programming min f(x) s.t. g i(x) 0 (i=1,…,m) g j(x)=0 (j=1,…, n), x ∈ Xand obtain various duality theorems. Where X is a Frechet space. f,g i(i=1,…, m) and h j(j=1, …, n) are functions from X to R 1.
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A semi-infinite programming problem is a mathematical programming problem with a finite number of variables and infinitely many constraints. Duality theories and generalized convexity concepts are important research topics in mathematical programming. In this paper, we discuss a fairly large number of paramet- ric duality results under various generalized （η,ρ）-invexity assumptions for a semi-infinite minmax fractional programming problem.
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In this paper, we present several parametric duality results under various generalized （a,v,p）-V- invexity assumptions for a semiinfinite multiobjective fractional programming problem.
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Supported by National Natural Science Foundation of China(71671122)China Postdoctoral Science Foundation Funded Project(2014M560185,2016T90203)+1 种基金Humanities and Social Science Research Fund of Ministry of Education of China(11YJC790006,16YJA790004)Tianjin Natural Science Foundation of China(15JCQNJC04000)
文摘This paper studies a dynamic mean-variance portfolio selection problem with random liability in the affine interest rate environment, where the financial market consists of three assets: one risk-free asset, one risky asset and one zero-coupon bond. Assume that short rate is driven by affine interest rate model and liability process is described by the drifted Brownian motion, in addition, stock price dynamics is affected by interest rate dynamics. The investors expect to look for an optimal strategy to minimize the variance of the terminal surplus for a given expected terminal surplus. The efficient strategy and the efficient frontier are explicitly obtained by applying dynamic programming principle and Lagrange duality theorem. A numerical example is given to illustrate our results and some economic implications are analyzed.
