This paper proposes a two-piece update of projected reduced Hessian algorithmwith nonmonotonic trust region strategy for solving nonlinear equality constrained optimizationproblems. In order to deal with large problem...This paper proposes a two-piece update of projected reduced Hessian algorithmwith nonmonotonic trust region strategy for solving nonlinear equality constrained optimizationproblems. In order to deal with large problems, a two-piece update of two-side projected reducedHessian is used to replace full Hessian matrix. By adopting the Fletcher's penalty function as themerit function, a nonmonotonic trust region strategy is suggested which does not require the meritfunction to reduce its value in every iteration. The two-piece update of projected reduced Hessianalgorithm which switches to nonmonotonic trust region technique possesses global convergence whilemaintaining a two-step Q-superlinear local convergence rate under some reasonable conditions.Furthermore, one step Q-superlinear local convergence rate can be obtained if at least one of theupdate formulas is updated at each iteration by an alternative update rule. The numerical experimentresults are reported to show the effectiveness of the proposed algorithm.展开更多
Whereas for smaller animals the eardrums are well-characterized as excitable membranes or drums, some animals such as several archosaurs feature, as a first approximation, a rather stiff elastic shell supported by an ...Whereas for smaller animals the eardrums are well-characterized as excitable membranes or drums, some animals such as several archosaurs feature, as a first approximation, a rather stiff elastic shell supported by an elastic ring. Mathematically, the theory of plates and shells is applicable but its governing equations overly complicate the modeling. Here the notion of tympanic structure is introduced as a generalization of “ordinary” tympanic membranes so as to account for sound perception as it occurs in archosaurs, such as birds and crocodilians. A mathematical model for the tympanic structure in many archosaurs called two-spring model implements this notion. The model is exactly soluble and solutions are presented in closed form and as a series expansion. Special emphasis is put onto offering an easy-to-apply model for describing experiments and performing numerical studies. The analytic treatment is supplemented by a discussion of the applicability of the two-spring model in auditory research. An elasticity-theoretic perspective of the two-spring model is given in the Appendix.展开更多
基金The author gratefully acknowledges the partial supports of the National Science Foundation of China Grant (10071050)Science Foundation of Shanghai Technical Sciences Committee Grant (02ZA14070) Science Foundation of Shanghai Education Committee Grant
文摘This paper proposes a two-piece update of projected reduced Hessian algorithmwith nonmonotonic trust region strategy for solving nonlinear equality constrained optimizationproblems. In order to deal with large problems, a two-piece update of two-side projected reducedHessian is used to replace full Hessian matrix. By adopting the Fletcher's penalty function as themerit function, a nonmonotonic trust region strategy is suggested which does not require the meritfunction to reduce its value in every iteration. The two-piece update of projected reduced Hessianalgorithm which switches to nonmonotonic trust region technique possesses global convergence whilemaintaining a two-step Q-superlinear local convergence rate under some reasonable conditions.Furthermore, one step Q-superlinear local convergence rate can be obtained if at least one of theupdate formulas is updated at each iteration by an alternative update rule. The numerical experimentresults are reported to show the effectiveness of the proposed algorithm.
文摘Whereas for smaller animals the eardrums are well-characterized as excitable membranes or drums, some animals such as several archosaurs feature, as a first approximation, a rather stiff elastic shell supported by an elastic ring. Mathematically, the theory of plates and shells is applicable but its governing equations overly complicate the modeling. Here the notion of tympanic structure is introduced as a generalization of “ordinary” tympanic membranes so as to account for sound perception as it occurs in archosaurs, such as birds and crocodilians. A mathematical model for the tympanic structure in many archosaurs called two-spring model implements this notion. The model is exactly soluble and solutions are presented in closed form and as a series expansion. Special emphasis is put onto offering an easy-to-apply model for describing experiments and performing numerical studies. The analytic treatment is supplemented by a discussion of the applicability of the two-spring model in auditory research. An elasticity-theoretic perspective of the two-spring model is given in the Appendix.
