A new algorithm for inequality constrained optimization is presented, which solves a linear programming subproblem and a quadratic subproblem at each iteration. The algorithm can circumvent the difficulties associated...A new algorithm for inequality constrained optimization is presented, which solves a linear programming subproblem and a quadratic subproblem at each iteration. The algorithm can circumvent the difficulties associated with the possible inconsistency of QP subproblem of the original SQP method. Moreover, the algorithm can converge to a point which satisfies a certain first-order necessary condition even if the original problem is itself infeasible. Under certain condition, some global convergence results are proved and local superlinear convergence results are also obtained. Preliminary numerical results are reported.展开更多
The precursors of dipole blocking are obtained by a numerical approach based upon a quasi-geostrophic barotropic planetary- to synoptic-scale interaction model without topography and with a localized synoptic-scale wa...The precursors of dipole blocking are obtained by a numerical approach based upon a quasi-geostrophic barotropic planetary- to synoptic-scale interaction model without topography and with a localized synoptic-scale wave-maker. The optimization problem related to the precursors of blocking is formulated and the nonlinear optimization method is used to examine the optimal synoptic-scale initial field successfully. The results show that the prominent characteristics of the optimal synoptic-scale initial field are that the synoptic-scale wave train structures exist upstream of the incipient blocking. In addition, the large-scale low/high eddy-forcing pattern upstream of the incipient blocking is an essential precondition for the onset of dipole blocking.展开更多
This paper gives a new subspace correction algorithm for nonlinear unconstrained convex optimization problems based on the multigrid approach proposed by S. Nash in 2000 and the subspace correction algorithm proposed ...This paper gives a new subspace correction algorithm for nonlinear unconstrained convex optimization problems based on the multigrid approach proposed by S. Nash in 2000 and the subspace correction algorithm proposed by X. Tai and J. Xu in 2001. Under some reasonable assumptions, we obtain the convergence as well as a convergence rate estimate for the algorithm. Numerical results show that the algorithm is effective.展开更多
This paper presents a trust region two phase model algorithm for solving the equality and bound constrained nonlinear optimization problem. A concept of substationary point is given. Under suitable assumptions,the gl...This paper presents a trust region two phase model algorithm for solving the equality and bound constrained nonlinear optimization problem. A concept of substationary point is given. Under suitable assumptions,the global convergence of this algorithm is proved without assuming the linear independence of the gradient of active constraints. A numerical example is also presented.展开更多
A new two-level subspace method is proposed for solving the general unconstrained minimization formulations discretized from infinite-dimensional optimization problems. At each iteration, the algorithm executes either...A new two-level subspace method is proposed for solving the general unconstrained minimization formulations discretized from infinite-dimensional optimization problems. At each iteration, the algorithm executes either a direct step on the current level or a coarse subspace correction step. In the coarse subspace correction step, we augment the traditional coarse grid space by a two-dimensional subspace spanned by the coordinate direction and the gradient direction at the current point. Global convergence is proved and convergence rate is studied under some mild conditions on the discretized functions. Preliminary numerical experiments on a few variational problems show that our two-level subspace method is promising.展开更多
A numerical embedding method was proposed for solving the nonlinear optimization problem. By using the nonsmooth theory, the existence and the continuation of the following path for the corresponding homotopy equation...A numerical embedding method was proposed for solving the nonlinear optimization problem. By using the nonsmooth theory, the existence and the continuation of the following path for the corresponding homotopy equations were proved. Therefore the basic theory for the algorithm of the numerical embedding method for solving the non-linear optimization problem was established. Based on the theoretical results, a numerical embedding algorithm was designed for solving the nonlinear optimization problem, and prove its convergence carefully. Numerical experiments show that the algorithm is effective.展开更多
基金This work is supported in part by the National Natural Science Foundation of China (Grant No. 10171055).
文摘A new algorithm for inequality constrained optimization is presented, which solves a linear programming subproblem and a quadratic subproblem at each iteration. The algorithm can circumvent the difficulties associated with the possible inconsistency of QP subproblem of the original SQP method. Moreover, the algorithm can converge to a point which satisfies a certain first-order necessary condition even if the original problem is itself infeasible. Under certain condition, some global convergence results are proved and local superlinear convergence results are also obtained. Preliminary numerical results are reported.
基金This paper was supported by the Outstanding Youth Natural Science Foundation of China(Grant No.40325016)the Teaching and Research Award Program for Outstanding Young Teachers in Higher Education Institutions of MOE,PRC(TRAPOYT)the National Natural Science Foundation of China(Grant No.40175011).
文摘The precursors of dipole blocking are obtained by a numerical approach based upon a quasi-geostrophic barotropic planetary- to synoptic-scale interaction model without topography and with a localized synoptic-scale wave-maker. The optimization problem related to the precursors of blocking is formulated and the nonlinear optimization method is used to examine the optimal synoptic-scale initial field successfully. The results show that the prominent characteristics of the optimal synoptic-scale initial field are that the synoptic-scale wave train structures exist upstream of the incipient blocking. In addition, the large-scale low/high eddy-forcing pattern upstream of the incipient blocking is an essential precondition for the onset of dipole blocking.
基金Supported by the National Nature Science Foundation of China (No.10971058)the Key Project of Chinese Ministry of Education (No.309023)
文摘This paper gives a new subspace correction algorithm for nonlinear unconstrained convex optimization problems based on the multigrid approach proposed by S. Nash in 2000 and the subspace correction algorithm proposed by X. Tai and J. Xu in 2001. Under some reasonable assumptions, we obtain the convergence as well as a convergence rate estimate for the algorithm. Numerical results show that the algorithm is effective.
文摘This paper presents a trust region two phase model algorithm for solving the equality and bound constrained nonlinear optimization problem. A concept of substationary point is given. Under suitable assumptions,the global convergence of this algorithm is proved without assuming the linear independence of the gradient of active constraints. A numerical example is also presented.
文摘A new two-level subspace method is proposed for solving the general unconstrained minimization formulations discretized from infinite-dimensional optimization problems. At each iteration, the algorithm executes either a direct step on the current level or a coarse subspace correction step. In the coarse subspace correction step, we augment the traditional coarse grid space by a two-dimensional subspace spanned by the coordinate direction and the gradient direction at the current point. Global convergence is proved and convergence rate is studied under some mild conditions on the discretized functions. Preliminary numerical experiments on a few variational problems show that our two-level subspace method is promising.
文摘A numerical embedding method was proposed for solving the nonlinear optimization problem. By using the nonsmooth theory, the existence and the continuation of the following path for the corresponding homotopy equations were proved. Therefore the basic theory for the algorithm of the numerical embedding method for solving the non-linear optimization problem was established. Based on the theoretical results, a numerical embedding algorithm was designed for solving the nonlinear optimization problem, and prove its convergence carefully. Numerical experiments show that the algorithm is effective.
