In this paper, the existence theorem of the cone weak subdifferential of set valued mapping in locally convex topological vector space is proved. Received March 30,1998. 1991 MR Subject Classification: 4...In this paper, the existence theorem of the cone weak subdifferential of set valued mapping in locally convex topological vector space is proved. Received March 30,1998. 1991 MR Subject Classification: 47H17,90C29.展开更多
Line-commutated converter (LCC)-based high-voltage DC (HVDC) systems have been integrated with bulk AC power grids for interregional transmission of renewable power. The nonlinear LCC model brings additional nonconvex...Line-commutated converter (LCC)-based high-voltage DC (HVDC) systems have been integrated with bulk AC power grids for interregional transmission of renewable power. The nonlinear LCC model brings additional nonconvexity to optimal power flow (OPF) of hybrid AC-DC power grids. A convexification method for the LCC station model could address such nonconvexity but has rarely been discussed. We devise an equivalent reformulation for classical LCC station models that facilitates second-order cone convex relaxation for the OPF of LCC-based AC-DC power grids. We also propose sufficient conditions for exactness of convex relaxation with its proof. Equivalence of the proposed LCC station models and properties, exactness, and effectiveness of convex relaxation are verified using four numerical simulations. Simulation results demonstrate a globally optimal solution of the original OPF can be efficiently obtained from relaxed model.展开更多
The Hardy space Hpis not locally convex if 0 < p < 1, even though its conjugate space(Hp) separates the points of Hp. But then it is locally p-convex, and its conjugate cone(Hp) p is large enough to separate the...The Hardy space Hpis not locally convex if 0 < p < 1, even though its conjugate space(Hp) separates the points of Hp. But then it is locally p-convex, and its conjugate cone(Hp) p is large enough to separate the points of Hp. In this case, the conjugate cone can be used to replace its conjugate space to set up the duality theory in the p-convex analysis. This paper deals with the representation problem of the conjugate cone(Hp) p of Hpfor 0 < p ≤ 1, and obtains the subrepresentation theorem(Hp) p L∞(T, C p).展开更多
The popularity of direct current(DC)networks have made their optimal power flow(OPF)problem a hot topic.With the proliferation of distributed generation,the many problems of centralized optimization methods,such as si...The popularity of direct current(DC)networks have made their optimal power flow(OPF)problem a hot topic.With the proliferation of distributed generation,the many problems of centralized optimization methods,such as single point failure and slow response speed,have led to utilization of measures such as distributed OPF methods.The OPF problem is non-convex,which makes it difficult to obtain an optimal solution.The second-order cone programming(SOCP)relaxation method is widely utilized to make the OPF problem convex.It is difficult to guarantee its exactness,especially when line constraints are considered.This paper proposes a penalty based ADMM approach using difference-of-convex programming(DCP)to solve the non-convex OPF problem in a distributed manner.The algorithm is composed of distributed x iteration,z iteration and A,/i iteration.Specifically,in the distributed z iteration,the active power flow injection equation of each line is formulated as a difference of two convex functions,and then the SOCP relaxation is given in a different form.If the SOCP relaxation is inexact,a penalty item is added to drive the solution to be feasible.Then,an optimal solution can be obtained using a local nonlinear programming method.Finally,simulations on a 14-bus system and the IEEE 123-bus system validate the effectiveness of the proposed approach.展开更多
This article proposes a method for fitting models subject to a convex and log-convex constraint on the probability vector of a product multinomial （binomial） distribution. We present an iterative algorithm for findi...This article proposes a method for fitting models subject to a convex and log-convex constraint on the probability vector of a product multinomial （binomial） distribution. We present an iterative algorithm for finding the restricted maximum likelihood estimates （MLEs） of the probability vector and show that the algorithm converges to the true solution. Some examples are discussed to illustrate the method.展开更多
A multicriterion clustering model with cone dominated structure is established and the concept of cone-efficient clustering is put forward. The properties of cone-efficient clustering are disscussed, and a method to s...A multicriterion clustering model with cone dominated structure is established and the concept of cone-efficient clustering is put forward. The properties of cone-efficient clustering are disscussed, and a method to solve multicriterion clustering is put forward.The model of Ref.[3] is a special case of that proposed in this paper.展开更多
This paper deals with the locallyβ-convex analysis that generalizes the locally convex analysis. The second separation theorem in locallyβ-convex spaces, the Minkowski theorem and the Krein-Milman theorem in theβ-c...This paper deals with the locallyβ-convex analysis that generalizes the locally convex analysis. The second separation theorem in locallyβ-convex spaces, the Minkowski theorem and the Krein-Milman theorem in theβ-convex analysis are given. Moreover, it is obtained that the U F-boundedness and the U B-boundedness in its conjugate cone are equivalent if and only if X is subcomplete.展开更多
We develop first order optimality conditions for constrained vector optimization. The partial orders for the objective and the constraints are induced by closed and convex cones with nonempty interior. After presentin...We develop first order optimality conditions for constrained vector optimization. The partial orders for the objective and the constraints are induced by closed and convex cones with nonempty interior. After presenting some well known existence results for these problems, based on a scalarization approach, we establish necessity of the optimality conditions under a Slater-like constraint qualification, and then sufficiency for the K-convex case. We present two alternative sets of optimality conditions, with the same properties in connection with necessity and sufficiency, but which are different with respect to the dimension of the spaces to which the dual multipliers belong. We introduce a duality scheme, with a point-to-set dual objective, for which strong duality holds. Some examples and open problems for future research are also presented.展开更多
文摘In this paper, the existence theorem of the cone weak subdifferential of set valued mapping in locally convex topological vector space is proved. Received March 30,1998. 1991 MR Subject Classification: 47H17,90C29.
基金supported by the National Natural Science Foundation of China under Grant 52177086the Fundamental Research Funds for the Central Universities under Grant 2023ZYGXZR063the Science and Technology Program of Guizhou Power Grid Coorperation under Grant GZKJXM20222386.
文摘Line-commutated converter (LCC)-based high-voltage DC (HVDC) systems have been integrated with bulk AC power grids for interregional transmission of renewable power. The nonlinear LCC model brings additional nonconvexity to optimal power flow (OPF) of hybrid AC-DC power grids. A convexification method for the LCC station model could address such nonconvexity but has rarely been discussed. We devise an equivalent reformulation for classical LCC station models that facilitates second-order cone convex relaxation for the OPF of LCC-based AC-DC power grids. We also propose sufficient conditions for exactness of convex relaxation with its proof. Equivalence of the proposed LCC station models and properties, exactness, and effectiveness of convex relaxation are verified using four numerical simulations. Simulation results demonstrate a globally optimal solution of the original OPF can be efficiently obtained from relaxed model.
基金supported by the National Natural Science Foundation of China(No.10871141)
文摘The Hardy space Hpis not locally convex if 0 < p < 1, even though its conjugate space(Hp) separates the points of Hp. But then it is locally p-convex, and its conjugate cone(Hp) p is large enough to separate the points of Hp. In this case, the conjugate cone can be used to replace its conjugate space to set up the duality theory in the p-convex analysis. This paper deals with the representation problem of the conjugate cone(Hp) p of Hpfor 0 < p ≤ 1, and obtains the subrepresentation theorem(Hp) p L∞(T, C p).
基金supported in part by the National Natural Science Foundation of China(51477070)National Key Research and Development Program of China(2018YFB0905000)Jiangsu Electric Power Company(J2019087).
文摘The popularity of direct current(DC)networks have made their optimal power flow(OPF)problem a hot topic.With the proliferation of distributed generation,the many problems of centralized optimization methods,such as single point failure and slow response speed,have led to utilization of measures such as distributed OPF methods.The OPF problem is non-convex,which makes it difficult to obtain an optimal solution.The second-order cone programming(SOCP)relaxation method is widely utilized to make the OPF problem convex.It is difficult to guarantee its exactness,especially when line constraints are considered.This paper proposes a penalty based ADMM approach using difference-of-convex programming(DCP)to solve the non-convex OPF problem in a distributed manner.The algorithm is composed of distributed x iteration,z iteration and A,/i iteration.Specifically,in the distributed z iteration,the active power flow injection equation of each line is formulated as a difference of two convex functions,and then the SOCP relaxation is given in a different form.If the SOCP relaxation is inexact,a penalty item is added to drive the solution to be feasible.Then,an optimal solution can be obtained using a local nonlinear programming method.Finally,simulations on a 14-bus system and the IEEE 123-bus system validate the effectiveness of the proposed approach.
基金Supported by the National Natural Science Foundation of China(No.11071008)Scientific Foundations of Beijing Jiaotong University(No.2012JBM105)
文摘This article proposes a method for fitting models subject to a convex and log-convex constraint on the probability vector of a product multinomial （binomial） distribution. We present an iterative algorithm for finding the restricted maximum likelihood estimates （MLEs） of the probability vector and show that the algorithm converges to the true solution. Some examples are discussed to illustrate the method.
文摘A multicriterion clustering model with cone dominated structure is established and the concept of cone-efficient clustering is put forward. The properties of cone-efficient clustering are disscussed, and a method to solve multicriterion clustering is put forward.The model of Ref.[3] is a special case of that proposed in this paper.
文摘This paper deals with the locallyβ-convex analysis that generalizes the locally convex analysis. The second separation theorem in locallyβ-convex spaces, the Minkowski theorem and the Krein-Milman theorem in theβ-convex analysis are given. Moreover, it is obtained that the U F-boundedness and the U B-boundedness in its conjugate cone are equivalent if and only if X is subcomplete.
基金a post-doctoral fellowship within the Department of Mathematics of the University of Haifa and by FAPERJ (Grant No.E-26/152.107/1990-Bolsa)Partially supported by CNP_q (Grant No.301280/86).Partially supported by CNP_q (Grant No.3002748/2002-4)
文摘We develop first order optimality conditions for constrained vector optimization. The partial orders for the objective and the constraints are induced by closed and convex cones with nonempty interior. After presenting some well known existence results for these problems, based on a scalarization approach, we establish necessity of the optimality conditions under a Slater-like constraint qualification, and then sufficiency for the K-convex case. We present two alternative sets of optimality conditions, with the same properties in connection with necessity and sufficiency, but which are different with respect to the dimension of the spaces to which the dual multipliers belong. We introduce a duality scheme, with a point-to-set dual objective, for which strong duality holds. Some examples and open problems for future research are also presented.
