A kind of mathematical programs with equilibrium constraints （MPEC） is studied. By using the idea of successive approximation, a smoothing nonlinear programming, which is equivalent to the MPEC problem, is proposed....A kind of mathematical programs with equilibrium constraints （MPEC） is studied. By using the idea of successive approximation, a smoothing nonlinear programming, which is equivalent to the MPEC problem, is proposed. Thereby, it is ensured that some classical optimization methods can be applied for the MPEC problem. In the end, two algorithm models are proposed with the detail analysis of the global convergence.展开更多
In this paper, we describe a successive approximation and smooth sequential quadratic programming （SQP） method for mathematical programs with nonlinear complementarity constraints （MPCC）. We introduce a class of s...In this paper, we describe a successive approximation and smooth sequential quadratic programming （SQP） method for mathematical programs with nonlinear complementarity constraints （MPCC）. We introduce a class of smooth programs to approximate the MPCC. Using an 11 penalty function, the line search assures global convergence, while the superlinear convergence rate is shown under the strictly complementary and second-order sufficient conditions. Moreover, we prove that the current iterated point is an exact stationary point of the mathematical programs with equilibrium constraints （MPEC） when the algorithm terminates finitely.展开更多
In this paper, a new method for solving a mathematical programming problem with linearly complementarity constraints (MPLCC) is introduced, which applies the Levenberg-Marquardt (L-M) method to solve the B-stationary ...In this paper, a new method for solving a mathematical programming problem with linearly complementarity constraints (MPLCC) is introduced, which applies the Levenberg-Marquardt (L-M) method to solve the B-stationary condition of original problem. Under the MPEC-LICQ, the proposed method is proved convergent to B-stationary point of MPLCC.展开更多
This article discusses feasibility conditions in mathematical programs with equilibrium constraints （MPECs）. The authors prove that two sufficient conditions guarantee the feasibility of these MPECs. The authors sho...This article discusses feasibility conditions in mathematical programs with equilibrium constraints （MPECs）. The authors prove that two sufficient conditions guarantee the feasibility of these MPECs. The authors show that the two feasibility conditions are different from the feasibility condition in [2, 3], and show that the sufficient condition in [3] is stronger than that in [2].展开更多
This paper discusses a special class of mathematical programs with equilibrium constraints. At first, by using a generalized complementarity function, the discussed problem is transformed into a family of general nonl...This paper discusses a special class of mathematical programs with equilibrium constraints. At first, by using a generalized complementarity function, the discussed problem is transformed into a family of general nonlinear optimization problems containing additional variable μ. Furthermore, combining the idea of penalty function, an auxiliary problem with inequality constraints is presented. And then, by providing explicit searching direction, we establish a new conjugate projection gradient method for optimization with nonlinear complementarity constraints. Under some suitable conditions, the proposed method is proved to possess global and superlinear convergence rate.展开更多
Demand response(DR)using shared energy storage systems(ESSs)is an appealing method to save electricity bills for users under demand charge and time-of-use(TOU)price.A novel Stackelberg-game-based ESS sharing scheme is...Demand response(DR)using shared energy storage systems(ESSs)is an appealing method to save electricity bills for users under demand charge and time-of-use(TOU)price.A novel Stackelberg-game-based ESS sharing scheme is proposed and analyzed in this study.In this scheme,the interactions between selfish users and an operator are characterized as a Stackelberg game.Operator holds a large-scale ESS that is shared among users in the form of energy transactions.It sells energy to users and sets the selling price first.It maximizes its profit through optimal pricing and ESS dispatching.Users purchase some energy from operator for the reduction of their demand charges after operator's selling price is announced.This game-theoretic ESS sharing scheme is characterized and analyzed by formulating and solving a bi-level optimization model.The upper-level optimization maximizes operator's profit and the lower-level optimization minimizes users'costs.The bi-level model is transformed and linearized into a mixed-integer linear programming(MILP)model using the mathematical programming with equilibrium constraints(MPEC)method and model linearizing techniques.Case studies with actual data are carried out to explore the economic performances of the proposed ESS sharing scheme.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
文中提出一种智能电网环境下可控负荷优化调度的双层优化模型。上层是可控负荷聚合器的优化问题,其目标是通过优化调度3类可控负荷的方式最小化购电成本;下层是电网优化问题,该问题提供电网实时电价给上层优化问题。文中将电网优化问题...文中提出一种智能电网环境下可控负荷优化调度的双层优化模型。上层是可控负荷聚合器的优化问题,其目标是通过优化调度3类可控负荷的方式最小化购电成本;下层是电网优化问题,该问题提供电网实时电价给上层优化问题。文中将电网优化问题的KKT条件作为可控负荷优化问题的均衡约束,双层优化问题转换为具有均衡约束的数学规划(Mathematical Program with Equilibrium Constraints,MPEC)问题来求解。算例仿真反映了提出的调度策略的基本特征。展开更多
基金project supported by the National Natural Science Foundation of China(Nos.10501009 and 60471039)the Natural Science Foundation of Guangxi Province(No.0728206)
文摘A kind of mathematical programs with equilibrium constraints （MPEC） is studied. By using the idea of successive approximation, a smoothing nonlinear programming, which is equivalent to the MPEC problem, is proposed. Thereby, it is ensured that some classical optimization methods can be applied for the MPEC problem. In the end, two algorithm models are proposed with the detail analysis of the global convergence.
基金supported by the National Natural Science Foundation of China (Nos.10501009,10771040)the Natural Science Foundation of Guangxi Province of China (Nos.0728206,0640001)the China Postdoctoral Science Foundation (No.20070410228)
文摘In this paper, we describe a successive approximation and smooth sequential quadratic programming （SQP） method for mathematical programs with nonlinear complementarity constraints （MPCC）. We introduce a class of smooth programs to approximate the MPCC. Using an 11 penalty function, the line search assures global convergence, while the superlinear convergence rate is shown under the strictly complementary and second-order sufficient conditions. Moreover, we prove that the current iterated point is an exact stationary point of the mathematical programs with equilibrium constraints （MPEC） when the algorithm terminates finitely.
文摘In this paper, a new method for solving a mathematical programming problem with linearly complementarity constraints (MPLCC) is introduced, which applies the Levenberg-Marquardt (L-M) method to solve the B-stationary condition of original problem. Under the MPEC-LICQ, the proposed method is proved convergent to B-stationary point of MPLCC.
基金the National Natural Science Foundation of China(70271019)
文摘This article discusses feasibility conditions in mathematical programs with equilibrium constraints （MPECs）. The authors prove that two sufficient conditions guarantee the feasibility of these MPECs. The authors show that the two feasibility conditions are different from the feasibility condition in [2, 3], and show that the sufficient condition in [3] is stronger than that in [2].
文摘This paper discusses a special class of mathematical programs with equilibrium constraints. At first, by using a generalized complementarity function, the discussed problem is transformed into a family of general nonlinear optimization problems containing additional variable μ. Furthermore, combining the idea of penalty function, an auxiliary problem with inequality constraints is presented. And then, by providing explicit searching direction, we establish a new conjugate projection gradient method for optimization with nonlinear complementarity constraints. Under some suitable conditions, the proposed method is proved to possess global and superlinear convergence rate.
基金supported by the National Natural Science Foundation of China(U21A20478)Zhejiang Provincial Nature Science Foundation of China(LZ21F030004)Key-Area Research and Development Program of Guangdong Province(2018B010107002)。
文摘Demand response(DR)using shared energy storage systems(ESSs)is an appealing method to save electricity bills for users under demand charge and time-of-use(TOU)price.A novel Stackelberg-game-based ESS sharing scheme is proposed and analyzed in this study.In this scheme,the interactions between selfish users and an operator are characterized as a Stackelberg game.Operator holds a large-scale ESS that is shared among users in the form of energy transactions.It sells energy to users and sets the selling price first.It maximizes its profit through optimal pricing and ESS dispatching.Users purchase some energy from operator for the reduction of their demand charges after operator's selling price is announced.This game-theoretic ESS sharing scheme is characterized and analyzed by formulating and solving a bi-level optimization model.The upper-level optimization maximizes operator's profit and the lower-level optimization minimizes users'costs.The bi-level model is transformed and linearized into a mixed-integer linear programming(MILP)model using the mathematical programming with equilibrium constraints(MPEC)method and model linearizing techniques.Case studies with actual data are carried out to explore the economic performances of the proposed ESS sharing scheme.
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.
文摘文中提出一种智能电网环境下可控负荷优化调度的双层优化模型。上层是可控负荷聚合器的优化问题,其目标是通过优化调度3类可控负荷的方式最小化购电成本;下层是电网优化问题,该问题提供电网实时电价给上层优化问题。文中将电网优化问题的KKT条件作为可控负荷优化问题的均衡约束,双层优化问题转换为具有均衡约束的数学规划(Mathematical Program with Equilibrium Constraints,MPEC)问题来求解。算例仿真反映了提出的调度策略的基本特征。
