Focuses on a study which determined the geometry meaning of the maxima of the CDT mathematical subproblem's dual function. Properties of trust region subproblem; Approximation of the CDT feasible region; Relations...Focuses on a study which determined the geometry meaning of the maxima of the CDT mathematical subproblem's dual function. Properties of trust region subproblem; Approximation of the CDT feasible region; Relations between the CDT problem and the trust region problem; Illustration of the geometry meaning of the jump parameter.展开更多
In this paper, we discuss the vortex structure of the superconducting thin films placed in a magnetic field. We show that the global minimizer of the functional modelling the superconducting thin films has a bounded n...In this paper, we discuss the vortex structure of the superconducting thin films placed in a magnetic field. We show that the global minimizer of the functional modelling the superconducting thin films has a bounded number of vortices when the applied magnetic field hex 〈 Hc1 ＋ K log ｜ logε｜ where Hc1 is the lower critical field of the film obtained by Ding and Du in SIAM J. Math. Anal., 2002. The locations of the vortices are also given.展开更多
An exact augmented Lagrangian function for the nonlinear nonconvex programming problems with inequality constraints was discussed. Under suitable hypotheses, the relationship was established between the local unconstr...An exact augmented Lagrangian function for the nonlinear nonconvex programming problems with inequality constraints was discussed. Under suitable hypotheses, the relationship was established between the local unconstrained minimizers of the augmented Lagrangian function on the space of problem variables and the local minimizers of the original constrained problem. Furthermore, under some assumptions, the relationship was also established between the global solutions of the augmented Lagrangian function on some compact subset of the space of problem variables and the global solutions of the constrained problem. Therefore, f^om the theoretical point of view, a solution of the inequality constrained problem and the corresponding values of the Lagrange multipliers can be found by the well-known method of multipliers which resort to the unconstrained minimization of the augmented Lagrangian function presented.展开更多
基金Research partially supported by Chinese NSF grants 19525101, 19731010 and State key project 96-221-04-02-02.
文摘Focuses on a study which determined the geometry meaning of the maxima of the CDT mathematical subproblem's dual function. Properties of trust region subproblem; Approximation of the CDT feasible region; Relations between the CDT problem and the trust region problem; Illustration of the geometry meaning of the jump parameter.
基金partially supported by the Natural Science Foundation of China (Nos. 19971030, 10471050)the Natural Science Foundation of Guangdong Province (No. 000671, No. 031495)partially supported by a grant from HKRGC
文摘In this paper, we discuss the vortex structure of the superconducting thin films placed in a magnetic field. We show that the global minimizer of the functional modelling the superconducting thin films has a bounded number of vortices when the applied magnetic field hex 〈 Hc1 ＋ K log ｜ logε｜ where Hc1 is the lower critical field of the film obtained by Ding and Du in SIAM J. Math. Anal., 2002. The locations of the vortices are also given.
文摘An exact augmented Lagrangian function for the nonlinear nonconvex programming problems with inequality constraints was discussed. Under suitable hypotheses, the relationship was established between the local unconstrained minimizers of the augmented Lagrangian function on the space of problem variables and the local minimizers of the original constrained problem. Furthermore, under some assumptions, the relationship was also established between the global solutions of the augmented Lagrangian function on some compact subset of the space of problem variables and the global solutions of the constrained problem. Therefore, f^om the theoretical point of view, a solution of the inequality constrained problem and the corresponding values of the Lagrange multipliers can be found by the well-known method of multipliers which resort to the unconstrained minimization of the augmented Lagrangian function presented.
基金The National Natural Science Foundation of China(No.10571137)The Great Natural Science Foundation of Henan University of Science and Technology(2005ZD06).
