Based on a smoothing symmetric disturbance FB-function,a smoothing inexact Newton method for solving the nonlinear complementarity problem with P0-function was proposed.It was proved that under mild conditions,the giv...Based on a smoothing symmetric disturbance FB-function,a smoothing inexact Newton method for solving the nonlinear complementarity problem with P0-function was proposed.It was proved that under mild conditions,the given algorithm performed global and superlinear convergence without strict complementarity.For the same linear complementarity problem(LCP),the algorithm needs similar iteration times to the literature.However,its accuracy is improved by at least 4 orders with calculation time reduced by almost 50%,and the iterative number is insensitive to the size of the LCP.Moreover,fewer iterations and shorter time are required for solving the problem by using inexact Newton methods for different initial points.展开更多
首先考虑以下的标准形式的线性规划问题(LP)及其相应的对偶规划(LD):(LP) min c^Tx,s.t.Ax=b,x≥0;(LD) max b^Ty,s.t.A^Ty+s=c,s≥0,其中A∈R^(m×n)(m≤n),c,x,s∈R^n,b,y∈R^m,并且rank(A)=m.以T表示相应于LP和LD中所有可行的x和...首先考虑以下的标准形式的线性规划问题(LP)及其相应的对偶规划(LD):(LP) min c^Tx,s.t.Ax=b,x≥0;(LD) max b^Ty,s.t.A^Ty+s=c,s≥0,其中A∈R^(m×n)(m≤n),c,x,s∈R^n,b,y∈R^m,并且rank(A)=m.以T表示相应于LP和LD中所有可行的x和(y,s)的集合.T^0={(x,y,s):(x,s)>0,(x,y,s)∈T}.由于近年来对线性规划内点方法所进行广泛和深入的研究,人们在理论上对各种不同形式的内点方法的计算复杂性、收敛性质等有较清楚的了解.大量的数值试验表明应用预纠正的原始-对偶内点方法(primal-dual method)展开更多
基金Supported by the National Natural Science Foundation of China(No.51205286)
文摘Based on a smoothing symmetric disturbance FB-function,a smoothing inexact Newton method for solving the nonlinear complementarity problem with P0-function was proposed.It was proved that under mild conditions,the given algorithm performed global and superlinear convergence without strict complementarity.For the same linear complementarity problem(LCP),the algorithm needs similar iteration times to the literature.However,its accuracy is improved by at least 4 orders with calculation time reduced by almost 50%,and the iterative number is insensitive to the size of the LCP.Moreover,fewer iterations and shorter time are required for solving the problem by using inexact Newton methods for different initial points.
文摘首先考虑以下的标准形式的线性规划问题(LP)及其相应的对偶规划(LD):(LP) min c^Tx,s.t.Ax=b,x≥0;(LD) max b^Ty,s.t.A^Ty+s=c,s≥0,其中A∈R^(m×n)(m≤n),c,x,s∈R^n,b,y∈R^m,并且rank(A)=m.以T表示相应于LP和LD中所有可行的x和(y,s)的集合.T^0={(x,y,s):(x,s)>0,(x,y,s)∈T}.由于近年来对线性规划内点方法所进行广泛和深入的研究,人们在理论上对各种不同形式的内点方法的计算复杂性、收敛性质等有较清楚的了解.大量的数值试验表明应用预纠正的原始-对偶内点方法(primal-dual method)
