Quasi-Newton (QN) equation plays a core role in contemporary nonlinear optimization. The traditional QN equation employs only the gradients, but ignores the function value information, which seems unreasonable. In thi...Quasi-Newton (QN) equation plays a core role in contemporary nonlinear optimization. The traditional QN equation employs only the gradients, but ignores the function value information, which seems unreasonable. In this paper, we consider a class of DFP method with new QN equations which use both gradient and function value infor- mation and ask very little additional computation. We give the condition of convergence and superlinear convergence for these methods. We also prove that under some line search conditions the DFP method with new QN equations is convergeot and superlinearly con- vergent.展开更多
The prior estimate and decay property of positive solutions are derived for a system of quasi- linear elliptic differential equations first. Hence, the result of non-existence for differential equation system of radia...The prior estimate and decay property of positive solutions are derived for a system of quasi- linear elliptic differential equations first. Hence, the result of non-existence for differential equation system of radially nonincreasing positive solutions is implied. By using this nonexistence result, blowup estimates for a class quasi-linear reaction-diffusion systems ( non-Newtonian filtration systems) are established, which extends the result of semi-linear reaction diffusion( Fujita type) systems.展开更多
The rate equations for the intracavity-frequency-doubled quasi-three-level lasers are developed. By normalizing the related parameters, it is shown that the general solution to the rate equations is dependent upon fou...The rate equations for the intracavity-frequency-doubled quasi-three-level lasers are developed. By normalizing the related parameters, it is shown that the general solution to the rate equations is dependent upon four dimensionless parameters: the normalized reabsorption loss, the pump to laser-mode size ratio, the normalized pump level, and a parameter written as nSHG, which is related to the ability of the nonlinear crystal to convert the fundamental to the second harmonic. By numerically solving these rate equations, a group of general curves are obtained to express the relations between the solution and the four dimensionless parameters.展开更多
A quasi-Newton method (QNM) for solving an unconstrained optimization problem in infinite dimensional spaces is presented in this paper. We apply the QNM algorithm to an identification problem for a nonlinear system o...A quasi-Newton method (QNM) for solving an unconstrained optimization problem in infinite dimensional spaces is presented in this paper. We apply the QNM algorithm to an identification problem for a nonlinear system of differential equations, that is, to identify the parameter vector q = q(t) appearing in the following system of differential equations, based on the measurement of the state , where is a measurement operator. We give two examples to show the algorithm.展开更多
A Quasi-Newton method in Infinite-dimensional Spaces (QNIS) for solving operator equations is presellted and the convergence of a sequence generated by QNIS is also proved in the paper. Next, we suggest a finite-dimen...A Quasi-Newton method in Infinite-dimensional Spaces (QNIS) for solving operator equations is presellted and the convergence of a sequence generated by QNIS is also proved in the paper. Next, we suggest a finite-dimensional implementation of QNIS and prove that the sequence defined by the finite-dimensional algorithm converges to the root of the original operator equation providing that the later exists and that the Frechet derivative of the governing operator is invertible. Finally, we apply QNIS to an inverse problem for a parabolic differential equation to illustrate the efficiency of the finite-dimensional algorithm.展开更多
基金This research is supported by the Research and Development Foundation of Shanghai Education Commission and Asia-Pacific Operatio
文摘Quasi-Newton (QN) equation plays a core role in contemporary nonlinear optimization. The traditional QN equation employs only the gradients, but ignores the function value information, which seems unreasonable. In this paper, we consider a class of DFP method with new QN equations which use both gradient and function value infor- mation and ask very little additional computation. We give the condition of convergence and superlinear convergence for these methods. We also prove that under some line search conditions the DFP method with new QN equations is convergeot and superlinearly con- vergent.
文摘The prior estimate and decay property of positive solutions are derived for a system of quasi- linear elliptic differential equations first. Hence, the result of non-existence for differential equation system of radially nonincreasing positive solutions is implied. By using this nonexistence result, blowup estimates for a class quasi-linear reaction-diffusion systems ( non-Newtonian filtration systems) are established, which extends the result of semi-linear reaction diffusion( Fujita type) systems.
文摘The rate equations for the intracavity-frequency-doubled quasi-three-level lasers are developed. By normalizing the related parameters, it is shown that the general solution to the rate equations is dependent upon four dimensionless parameters: the normalized reabsorption loss, the pump to laser-mode size ratio, the normalized pump level, and a parameter written as nSHG, which is related to the ability of the nonlinear crystal to convert the fundamental to the second harmonic. By numerically solving these rate equations, a group of general curves are obtained to express the relations between the solution and the four dimensionless parameters.
基金This research is partially supported by the National Natural Science Foundation of China(No. 69774012).
文摘A quasi-Newton method (QNM) for solving an unconstrained optimization problem in infinite dimensional spaces is presented in this paper. We apply the QNM algorithm to an identification problem for a nonlinear system of differential equations, that is, to identify the parameter vector q = q(t) appearing in the following system of differential equations, based on the measurement of the state , where is a measurement operator. We give two examples to show the algorithm.
文摘A Quasi-Newton method in Infinite-dimensional Spaces (QNIS) for solving operator equations is presellted and the convergence of a sequence generated by QNIS is also proved in the paper. Next, we suggest a finite-dimensional implementation of QNIS and prove that the sequence defined by the finite-dimensional algorithm converges to the root of the original operator equation providing that the later exists and that the Frechet derivative of the governing operator is invertible. Finally, we apply QNIS to an inverse problem for a parabolic differential equation to illustrate the efficiency of the finite-dimensional algorithm.
