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
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
An optimal dimension-down iterative algorithm （DDIA） is proposed for solving a mixed （continuous/ discrete） transportation network design problem （MNDP）, which is generally expressed as a mathematical programmin...An optimal dimension-down iterative algorithm （DDIA） is proposed for solving a mixed （continuous/ discrete） transportation network design problem （MNDP）, which is generally expressed as a mathematical programming with equilibrium constraints （MPEC）. The upper level of the MNDP aims to optimize the network performance via both the expansion of existing links and the addition of new candidate links, whereas the lower level is a traditional Wardrop user equilibrium （UE） model. The idea of the proposed DDIA is to reduce the dimensions of the problem. A group of variables （discrete/continuous） are fixed to altemately optimize another group of variables （continuous/discrete）. Some continuous network design problems （CNDPs） and discrete network design problems （DNDPs） are solved repeatedly until the optimal solution is obtained. A numerical example is given to demonstrate the efficiency of the proposed algorithm.展开更多
The command-and-control regulation is likely inefficient and costly.This study investigates a regional pollution control scheme with tax(RPCST)under which the central government sets the tax rate under a given polluta...The command-and-control regulation is likely inefficient and costly.This study investigates a regional pollution control scheme with tax(RPCST)under which the central government sets the tax rate under a given pollutant reduction quota and local governments determine their pollution removal rates based on the central government’s policy.First,a one-leader-multi-follower(OLMF)Stackelberg game model is formulated,in which the central government is the leader and the local governments are the followers.Then,a procedure based on bilevel programming and relaxation method is applied to solve the OLMF model.Finally,a case study analyzing the SO2 reduction of the Yangtze River Delta in China is conducted to demonstrate the effectiveness of the RPCST.The results show that RPCST works better than the current command-andcontrol scheme.Our analysis provides a guideline for governments to design optimal tax schemes to effectively solve the regional air pollution crisis.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
In this paper, we present a new trust region algorithm for a nonlinear bilevel programming problem by solving a series of its linear or quadratic approximation subproblems. For the nonlinear bilevel programming proble...In this paper, we present a new trust region algorithm for a nonlinear bilevel programming problem by solving a series of its linear or quadratic approximation subproblems. For the nonlinear bilevel programming problem in which the lower level programming problem is a strongly convex programming problem with linear constraints, we show that each accumulation point of the iterative sequence produced by this algorithm is a stationary point of the bilevel programming problem.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.
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The National Natural Science Foundation of China(No. 50908235 )China Postdoctoral Science Foundation (No.201003520)
文摘An optimal dimension-down iterative algorithm （DDIA） is proposed for solving a mixed （continuous/ discrete） transportation network design problem （MNDP）, which is generally expressed as a mathematical programming with equilibrium constraints （MPEC）. The upper level of the MNDP aims to optimize the network performance via both the expansion of existing links and the addition of new candidate links, whereas the lower level is a traditional Wardrop user equilibrium （UE） model. The idea of the proposed DDIA is to reduce the dimensions of the problem. A group of variables （discrete/continuous） are fixed to altemately optimize another group of variables （continuous/discrete）. Some continuous network design problems （CNDPs） and discrete network design problems （DNDPs） are solved repeatedly until the optimal solution is obtained. A numerical example is given to demonstrate the efficiency of the proposed algorithm.
基金supported by grants from the National Natural Science Foundation of China[grant numbers 71874108,71373155,72131007]the National Social Science Fund of China[grant numbers 18AZD005,16ZDA048]+1 种基金the Chinese Ministry of Education on the key projects of philosophy and social sciences[grant number 17JZD025]the Natural Science Foundation of Shanghai[grant number 22ZR1415900].
文摘The command-and-control regulation is likely inefficient and costly.This study investigates a regional pollution control scheme with tax(RPCST)under which the central government sets the tax rate under a given pollutant reduction quota and local governments determine their pollution removal rates based on the central government’s policy.First,a one-leader-multi-follower(OLMF)Stackelberg game model is formulated,in which the central government is the leader and the local governments are the followers.Then,a procedure based on bilevel programming and relaxation method is applied to solve the OLMF model.Finally,a case study analyzing the SO2 reduction of the Yangtze River Delta in China is conducted to demonstrate the effectiveness of the RPCST.The results show that RPCST works better than the current command-andcontrol scheme.Our analysis provides a guideline for governments to design optimal tax schemes to effectively solve the regional air pollution crisis.
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].
基金Supported by the National Natural Science Foundation of China(No.11171348,11171252 and 71232011)
文摘In this paper, we present a new trust region algorithm for a nonlinear bilevel programming problem by solving a series of its linear or quadratic approximation subproblems. For the nonlinear bilevel programming problem in which the lower level programming problem is a strongly convex programming problem with linear constraints, we show that each accumulation point of the iterative sequence produced by this algorithm is a stationary point of the bilevel programming problem.
