One class of effective methods for the optimization problem with inequality constraints are to transform the problem to a unconstrained optimization problem by constructing a smooth potential function. In this paper, ...One class of effective methods for the optimization problem with inequality constraints are to transform the problem to a unconstrained optimization problem by constructing a smooth potential function. In this paper, we modifies a dual algorithm for constrained optimization problems and establishes a corresponding improved dual algorithm; It is proved that the improved dual algorithm has the local Q-superlinear convergence; Finally, we performed numerical experimentation using the improved dual algorithm for many constrained optimization problems, the numerical results are reported to show that it is valid in practical computation.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Supported by the National 863 Project (2003AA002030)
文摘One class of effective methods for the optimization problem with inequality constraints are to transform the problem to a unconstrained optimization problem by constructing a smooth potential function. In this paper, we modifies a dual algorithm for constrained optimization problems and establishes a corresponding improved dual algorithm; It is proved that the improved dual algorithm has the local Q-superlinear convergence; Finally, we performed numerical experimentation using the improved dual algorithm for many constrained optimization problems, the numerical results are reported to show that it is valid in practical computation.
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.
