The Newton-Like algorithm with price estimation error in optimization flow control in network is analyzed. The estimation error is treated as inexactness of the gradient and the inexact descent direction is analyzed. ...The Newton-Like algorithm with price estimation error in optimization flow control in network is analyzed. The estimation error is treated as inexactness of the gradient and the inexact descent direction is analyzed. Based on the optimization theory, a sufficient condition for convergence of this algorithm with bounded price estimation error is obtained. Furthermore, even when this sufficient condition doesn＇t hold, this algorithm can also converge, provided a modified step size, and an attraction region is obtained. Based on Lasalle＇s invariance principle applied to a suitable Lyapunov function, the dynamic system described by this algorithm is proved to be global stability if the error is zero. And the Newton-Like algorithm with bounded price estimation error is also globally stable if the error satisfies the sufficient condition for convergence. All trajectories ultimately converge to the equilibrium point.展开更多
We provide convergence results and error estimates for Newton-like methods in generalized Banach spaces.The idea of a generalized norm is used whichis defined to be a map from a linear space into a partially ordered B...We provide convergence results and error estimates for Newton-like methods in generalized Banach spaces.The idea of a generalized norm is used whichis defined to be a map from a linear space into a partially ordered Banach space.Convergence results and error estimates are improved compared with the real norm theory.展开更多
We consider a blockwise extended system and an efficient quadratically convergent Newton-like method for approximations of simple (cubic) singular solutions of nonlinear problems with sparse properties.
Presents two algorithms for LC unconstrained optimization problems which use the second order Dini upper directional derivative. Simplicity of the methods to use and perform; Discussion of related properties of the it...Presents two algorithms for LC unconstrained optimization problems which use the second order Dini upper directional derivative. Simplicity of the methods to use and perform; Discussion of related properties of the iteration function.展开更多
In this paper, we present Newton-like methods (modified Newton method and modified secant method), which explore the special structure of the finitedifference approximation of fourth order to the nonlinear two-point b...In this paper, we present Newton-like methods (modified Newton method and modified secant method), which explore the special structure of the finitedifference approximation of fourth order to the nonlinear two-point boundary value problems At each iteration, modified secant method only calls and computes one function vector (i.e., no additional cast in function evaluations), and it has a R- convergence rate, and modified Newton method only calls two function vectors,and it has a Q-quadratic convergence rate. At last, our numerical results show the new methods are very effective.展开更多
基金Project supported by Key Industrial Projects of Major Science and Technology Projects of Zhejiang(No.2009C11023)Foundation of Zhejiang Educational Committee(No.Y200907886)Major High-Tech Industrialization Project of Jiaxing(No.2009BY10004)
基金supported in part by the National Outstanding Youth Foundation of P.R.China (60525303)the National Natural Science Foundation of P.R.China(60404022,60604004)+2 种基金the Natural Science Foundation of Hebei Province (102160)the special projects in mathematics funded by the Natural Science Foundation of Hebei Province(07M005)the NS of Education Office in Hebei Province (2004123).
文摘The Newton-Like algorithm with price estimation error in optimization flow control in network is analyzed. The estimation error is treated as inexactness of the gradient and the inexact descent direction is analyzed. Based on the optimization theory, a sufficient condition for convergence of this algorithm with bounded price estimation error is obtained. Furthermore, even when this sufficient condition doesn＇t hold, this algorithm can also converge, provided a modified step size, and an attraction region is obtained. Based on Lasalle＇s invariance principle applied to a suitable Lyapunov function, the dynamic system described by this algorithm is proved to be global stability if the error is zero. And the Newton-Like algorithm with bounded price estimation error is also globally stable if the error satisfies the sufficient condition for convergence. All trajectories ultimately converge to the equilibrium point.
文摘We provide convergence results and error estimates for Newton-like methods in generalized Banach spaces.The idea of a generalized norm is used whichis defined to be a map from a linear space into a partially ordered Banach space.Convergence results and error estimates are improved compared with the real norm theory.
文摘We consider a blockwise extended system and an efficient quadratically convergent Newton-like method for approximations of simple (cubic) singular solutions of nonlinear problems with sparse properties.
基金CNPq of Brazil and the National Natural Science Foundation of China.
文摘Presents two algorithms for LC unconstrained optimization problems which use the second order Dini upper directional derivative. Simplicity of the methods to use and perform; Discussion of related properties of the iteration function.
文摘In this paper, we present Newton-like methods (modified Newton method and modified secant method), which explore the special structure of the finitedifference approximation of fourth order to the nonlinear two-point boundary value problems At each iteration, modified secant method only calls and computes one function vector (i.e., no additional cast in function evaluations), and it has a R- convergence rate, and modified Newton method only calls two function vectors,and it has a Q-quadratic convergence rate. At last, our numerical results show the new methods are very effective.
