In this paper, nonautonomous models of Discrete Event Dynamic Systems (DEDS) are established by min-max function, reachability and observability are defined, the problem on cycle times assignment of DEDS, which corres...In this paper, nonautonomous models of Discrete Event Dynamic Systems (DEDS) are established by min-max function, reachability and observability are defined, the problem on cycle times assignment of DEDS, which corresponds with the important problem on poles assignment of linear systems, is studied. By Gunawardena et al.’Duality Theorem following results are obtained: Cycle times of system can be assigned under state feedback(or output feedback) if and only if system is reachable (or reachable and obserbable).展开更多
This paper considers the mathematical programs with equilibrium constraints(MPEC).It is well-known that,due to the existence of equilibrium constraints,the Mangasarian-Fromovitz constraint qualification does not hold ...This paper considers the mathematical programs with equilibrium constraints(MPEC).It is well-known that,due to the existence of equilibrium constraints,the Mangasarian-Fromovitz constraint qualification does not hold at any feasible point of MPEC and hence,in general,the developed numerical algorithms for standard nonlinear programming problems can not be applied to solve MPEC directly.During the past two decades,much research has been done to develop numerical algorithms and study optimality,stability,and sensitivity for MPEC.However,there are very few results on duality for MPEC in the literature.In this paper,we present a Wolfe-type duality for MPEC and,under some suitable conditions,we establish various duality theorems such as the weak duality,direct duality,converse duality,and strict converse duality theorems.We further show that a linear MPEC is equivalent to a linear programming problem in some sense.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
This paper deals with Nonconical Nonsmooth Multiobjective ProgrammingProblem. The generalized directional deriVate of a maPping w.r.t a binary relation andthe derivate of a binary relation are illtroduced and used as ...This paper deals with Nonconical Nonsmooth Multiobjective ProgrammingProblem. The generalized directional deriVate of a maPping w.r.t a binary relation andthe derivate of a binary relation are illtroduced and used as basic tools. The optimalityconditions 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
基金This research is supported by the National Key Project of Chinathe National Natural Science Foundation of China !69874040
文摘In this paper, nonautonomous models of Discrete Event Dynamic Systems (DEDS) are established by min-max function, reachability and observability are defined, the problem on cycle times assignment of DEDS, which corresponds with the important problem on poles assignment of linear systems, is studied. By Gunawardena et al.’Duality Theorem following results are obtained: Cycle times of system can be assigned under state feedback(or output feedback) if and only if system is reachable (or reachable and obserbable).
基金supported by the NSFC Grant(No.11401379)supported in part by the NSFC Grant(No.11431004)the China Postdoctoral Science Foundation(No.2014M550237)
文摘This paper considers the mathematical programs with equilibrium constraints(MPEC).It is well-known that,due to the existence of equilibrium constraints,the Mangasarian-Fromovitz constraint qualification does not hold at any feasible point of MPEC and hence,in general,the developed numerical algorithms for standard nonlinear programming problems can not be applied to solve MPEC directly.During the past two decades,much research has been done to develop numerical algorithms and study optimality,stability,and sensitivity for MPEC.However,there are very few results on duality for MPEC in the literature.In this paper,we present a Wolfe-type duality for MPEC and,under some suitable conditions,we establish various duality theorems such as the weak duality,direct duality,converse duality,and strict converse duality theorems.We further show that a linear MPEC is equivalent to a linear programming problem in some sense.
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.
基金The author gratefully acknowledges the partial supports of the National Science Foundation Grant(10071050)of China Science Foundation Grant of Shanghai Technical Sciences Committee
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This paper deals with Nonconical Nonsmooth Multiobjective ProgrammingProblem. The generalized directional deriVate of a maPping w.r.t a binary relation andthe derivate of a binary relation are illtroduced and used as basic tools. The optimalityconditions 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.
