Mathematical programs with complementarity constraints(MPCC) is an important subclass of MPEC.It is a natural way to solve MPCC by constructing a suitable approximation of the primal problem.In this paper,we propose a...Mathematical programs with complementarity constraints(MPCC) is an important subclass of MPEC.It is a natural way to solve MPCC by constructing a suitable approximation of the primal problem.In this paper,we propose a new smoothing method for MPCC by using the aggregation technique.A new SQP algorithm for solving the MPCC problem is presented.At each iteration,the master direction is computed by solving a quadratic program,and the revised direction for avoiding the Maratos effect is generated by an explicit formula.As the non-degeneracy condition holds and the smoothing parameter tends to zero,the proposed SQP algorithm converges globally to an S-stationary point of the MPEC problem,its convergence rate is superlinear.Some preliminary numerical results are reported.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
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 propose a Sample Average Approximation （SAA） method for a class of Stochastic Mathematical Programs with Complementarity Constraints （SMPCC） recently considered by Birbil, G/irkan and Listes [3]....In this paper, we propose a Sample Average Approximation （SAA） method for a class of Stochastic Mathematical Programs with Complementarity Constraints （SMPCC） recently considered by Birbil, G/irkan and Listes [3]. We study the statistical properties of obtained SAA estimators. In particular we show that under moderate conditions a sequence of weak stationary points of SAA programs converge to a weak stationary point of the true problem with probability approaching one at exponential rate as the sample size tends to infinity. To implement the SAA method more efficiently, we incorporate the method with some techniques such as Scholtes＇ regularization method and the well known smoothing NCP method. Some preliminary numerical results are reported.展开更多
馈线区段故障的快速准确辨识对于提升配电网可靠性与自愈性有重要作用。针对基于逻辑关系的间接故障定位方法在数值稳定性和决策效率上的不足,该文基于代数关系描述和互补约束理论构建了配电网故障区段定位的互补约束新模型,其优势在于...馈线区段故障的快速准确辨识对于提升配电网可靠性与自愈性有重要作用。针对基于逻辑关系的间接故障定位方法在数值稳定性和决策效率上的不足,该文基于代数关系描述和互补约束理论构建了配电网故障区段定位的互补约束新模型,其优势在于:1)避免了对群体智能算法的过分依赖,可采用数值稳定性好的梯度算法优化求解;2)利用互补约束条件将离散变量松弛为连续变量,降低了故障定位问题决策时的复杂性。在此基础上,提出基于扰动因子的故障定位模型光滑化求解算法。仿真表明,新模型和决策算法不仅能够实现馈线故障区段的准确高容错性辨识,且进行优化决策时具有数值稳定性好、优化效率高的优点,在大规模配电网故障定位中有良好的应用前景。Fast and exact feeder fault location method plays an important role in enhancing reliability and self-healing of distribution network.Logic relationship based conventional indirect fault location model and method has the drawbacks of excessive reliance on swarm intelligence algorithm in optimization computation,numerical optimization instability and low decision-making efficiency.In order to overcome the above shortcomings,on basis of algebra relationship description and complementary theory,a novel complementarity constraints fault location model is proposed as follows:1min()()1,0[(1),(2),,()],[(1),(2),,()],0,,i N S i N N f KB x x x NκκκN=?=???+=⊥=?==?≥∈∈?X∑X X X X X XκκκκRκR(1)Because the feasible points of the above complementarity constraints model can not satisfy the nonlinear programming constraint specification,the optimal solution can not be obtained by using the nonlinear programming to satisfy the Karush-Kuhn-Tucker(KKT)condition.In order to solve the novel fault location model effectively used by nonlinear programming directly,the Fischer-Burmeister auxiliary function with the perturbation factor is used to transform the complementarity constraints fault location model into a continuous smoothing model,which can satisfy the B-stability point.The smoothing model for fault location with complementarity constraints can be expressed as:212 2 2min(,,)()()()()11 2 0()()0[(1),(2),,()][(1),(2),,()][(1),(2),,()],0,N i N N F f i f x x x N N Nφφεφκκκεεε=?=+??=??+=??-++=??=?=?=??=?≥??∈∈?∑X X X XεX XκεX XκεεεκκεκRεR(2)In this model,the feasible point satisfies the nonlinear constraint specification,which can be solved by nonlinear programming directly.When the value of the perturbation factor tends to zero and the KKT extremum condition is established,the optimal decision vector of the fault location model can be obtained,so that the feeder fault section can be found.The correctness and effectiveness of the fault location model with complementarity constraints are verified by(sequence quadratic program)SQP in Matlab2010 a simulation platform.The simulation study shows that:1)The novel model of distribution network fault location based on the theory of complementarity constraints can effectively reflect the correlation characteristics between the causal devices,which can accurately locate the fault section of the feeder fault,and has high fault tolerance.2)The model is proposed based on relational algebra description modeling,so in optimization decision process can avoid the fault identification model excessive reliance on swarm intelligence algorithm in optimization computation,in which the gradient algorithm with good numerical stability can be used,which has the advantage in numerical stability.3)By through the feeder fault status information complementarity constraints conditions,the fault identification model can be transformed from discrete optimization space to continuous optimization space,which can effectively reduce the complexity of fault location model in optimization decision.4)The smoothing method based on the perturbation factor auxiliary penalty function can improve the non-smoothing characteristics of the complementarity constraints model,which can lead the optimal value to converge to the stable point,so as to accurately locate the feeder fault section.5)The novel fault location model and decision method proposed in this paper can be applied to the feeder fault location problem in large scale distribution network.展开更多
互补约束优化问题(mathematical program with complementarity constraints,简记MPCC)是一类重要的平衡约束优化问题.此类问题具有十分广泛的应用.采用光滑化策略,用一类几乎处处光滑函数替代互补约束,从而将MPCC转化为一系列非线性规...互补约束优化问题(mathematical program with complementarity constraints,简记MPCC)是一类重要的平衡约束优化问题.此类问题具有十分广泛的应用.采用光滑化策略,用一类几乎处处光滑函数替代互补约束,从而将MPCC转化为一系列非线性规划问题(nonlinear programming,简记NLP).给出迭代算法并对Mac MPEC数据库中的一些问题测试了算法的有效性.展开更多
基金supported by the National Natural Science Foundation of China(No.10861005)the Natural Science Foundation of Guangxi Province (No.0728206)the Innovation Project of Guangxi Graduate Education(No. 2009105950701M29).
文摘Mathematical programs with complementarity constraints(MPCC) is an important subclass of MPEC.It is a natural way to solve MPCC by constructing a suitable approximation of the primal problem.In this paper,we propose a new smoothing method for MPCC by using the aggregation technique.A new SQP algorithm for solving the MPCC problem is presented.At each iteration,the master direction is computed by solving a quadratic program,and the revised direction for avoiding the Maratos effect is generated by an explicit formula.As the non-degeneracy condition holds and the smoothing parameter tends to zero,the proposed SQP algorithm converges globally to an S-stationary point of the MPEC problem,its convergence rate is superlinear.Some preliminary numerical results are reported.
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.
文摘In this paper, we propose a Sample Average Approximation （SAA） method for a class of Stochastic Mathematical Programs with Complementarity Constraints （SMPCC） recently considered by Birbil, G/irkan and Listes [3]. We study the statistical properties of obtained SAA estimators. In particular we show that under moderate conditions a sequence of weak stationary points of SAA programs converge to a weak stationary point of the true problem with probability approaching one at exponential rate as the sample size tends to infinity. To implement the SAA method more efficiently, we incorporate the method with some techniques such as Scholtes＇ regularization method and the well known smoothing NCP method. Some preliminary numerical results are reported.
文摘馈线区段故障的快速准确辨识对于提升配电网可靠性与自愈性有重要作用。针对基于逻辑关系的间接故障定位方法在数值稳定性和决策效率上的不足,该文基于代数关系描述和互补约束理论构建了配电网故障区段定位的互补约束新模型,其优势在于:1)避免了对群体智能算法的过分依赖,可采用数值稳定性好的梯度算法优化求解;2)利用互补约束条件将离散变量松弛为连续变量,降低了故障定位问题决策时的复杂性。在此基础上,提出基于扰动因子的故障定位模型光滑化求解算法。仿真表明,新模型和决策算法不仅能够实现馈线故障区段的准确高容错性辨识,且进行优化决策时具有数值稳定性好、优化效率高的优点,在大规模配电网故障定位中有良好的应用前景。Fast and exact feeder fault location method plays an important role in enhancing reliability and self-healing of distribution network.Logic relationship based conventional indirect fault location model and method has the drawbacks of excessive reliance on swarm intelligence algorithm in optimization computation,numerical optimization instability and low decision-making efficiency.In order to overcome the above shortcomings,on basis of algebra relationship description and complementary theory,a novel complementarity constraints fault location model is proposed as follows:1min()()1,0[(1),(2),,()],[(1),(2),,()],0,,i N S i N N f KB x x x NκκκN=?=???+=⊥=?==?≥∈∈?X∑X X X X X XκκκκRκR(1)Because the feasible points of the above complementarity constraints model can not satisfy the nonlinear programming constraint specification,the optimal solution can not be obtained by using the nonlinear programming to satisfy the Karush-Kuhn-Tucker(KKT)condition.In order to solve the novel fault location model effectively used by nonlinear programming directly,the Fischer-Burmeister auxiliary function with the perturbation factor is used to transform the complementarity constraints fault location model into a continuous smoothing model,which can satisfy the B-stability point.The smoothing model for fault location with complementarity constraints can be expressed as:212 2 2min(,,)()()()()11 2 0()()0[(1),(2),,()][(1),(2),,()][(1),(2),,()],0,N i N N F f i f x x x N N Nφφεφκκκεεε=?=+??=??+=??-++=??=?=?=??=?≥??∈∈?∑X X X XεX XκεX XκεεεκκεκRεR(2)In this model,the feasible point satisfies the nonlinear constraint specification,which can be solved by nonlinear programming directly.When the value of the perturbation factor tends to zero and the KKT extremum condition is established,the optimal decision vector of the fault location model can be obtained,so that the feeder fault section can be found.The correctness and effectiveness of the fault location model with complementarity constraints are verified by(sequence quadratic program)SQP in Matlab2010 a simulation platform.The simulation study shows that:1)The novel model of distribution network fault location based on the theory of complementarity constraints can effectively reflect the correlation characteristics between the causal devices,which can accurately locate the fault section of the feeder fault,and has high fault tolerance.2)The model is proposed based on relational algebra description modeling,so in optimization decision process can avoid the fault identification model excessive reliance on swarm intelligence algorithm in optimization computation,in which the gradient algorithm with good numerical stability can be used,which has the advantage in numerical stability.3)By through the feeder fault status information complementarity constraints conditions,the fault identification model can be transformed from discrete optimization space to continuous optimization space,which can effectively reduce the complexity of fault location model in optimization decision.4)The smoothing method based on the perturbation factor auxiliary penalty function can improve the non-smoothing characteristics of the complementarity constraints model,which can lead the optimal value to converge to the stable point,so as to accurately locate the feeder fault section.5)The novel fault location model and decision method proposed in this paper can be applied to the feeder fault location problem in large scale distribution network.
文摘互补约束优化问题(mathematical program with complementarity constraints,简记MPCC)是一类重要的平衡约束优化问题.此类问题具有十分广泛的应用.采用光滑化策略,用一类几乎处处光滑函数替代互补约束,从而将MPCC转化为一系列非线性规划问题(nonlinear programming,简记NLP).给出迭代算法并对Mac MPEC数据库中的一些问题测试了算法的有效性.
