Let P（s, δ） be a sphere plant family described by the transfer function set where the coefficients of the denominator and numerator polynomials are affine in a real uncertain parameter vector δ satisfying the Eucl...Let P（s, δ） be a sphere plant family described by the transfer function set where the coefficients of the denominator and numerator polynomials are affine in a real uncertain parameter vector δ satisfying the Euclidean norm constraint ｜｜δ｜｜〈δ. The concept of stabilizability radius of P（s, δ） is introduced which is the norm bound δs for δ such that every member plant of P（s, δ） is stabilizable if and only if ｜｜δ｜｜〈δs. The stabilizability radius can be simply interpreted as the ＇largest sphere＇ around the nominal plant P（s,θ） such that P（s, δ） is stabilizable. The numerical method and the analytical method are presented to solve the stabilizability radius calculation problem of the sphere plants.展开更多
A methodology for topology optimization based on element independent nodal density(EIND) is developed.Nodal densities are implemented as the design variables and interpolated onto element space to determine the densit...A methodology for topology optimization based on element independent nodal density(EIND) is developed.Nodal densities are implemented as the design variables and interpolated onto element space to determine the density of any point with Shepard interpolation function.The influence of the diameter of interpolation is discussed which shows good robustness.The new approach is demonstrated on the minimum volume problem subjected to a displacement constraint.The rational approximation for material properties(RAMP) method and a dual programming optimization algorithm are used to penalize the intermediate density point to achieve nearly 0-1 solutions.Solutions are shown to meet stability,mesh dependence or non-checkerboard patterns of topology optimization without additional constraints.Finally,the computational efficiency is greatly improved by multithread parallel computing with OpenMP.展开更多
The recently improved finite order BFT Hamiltonian embedding method is applied to the two dimensional chiral bosons in non-commutative space. It is then systematically converted to a first class constraint model. Perf...The recently improved finite order BFT Hamiltonian embedding method is applied to the two dimensional chiral bosons in non-commutative space. It is then systematically converted to a first class constraint model. Performing the momentum integrations, the corresponding fully gauge symmetry Lagrangian as well as its partition function in phase space are obtained.展开更多
Some classical penalty function algorithms may not always be convergent under big penalty parameters in Matlab software,which makes them impossible to find out an optimal solution to constrained optimization problems....Some classical penalty function algorithms may not always be convergent under big penalty parameters in Matlab software,which makes them impossible to find out an optimal solution to constrained optimization problems.In this paper,a novel penalty function(called M-objective penalty function) with one penalty parameter added to both objective and constrained functions of inequality constrained optimization problems is proposed.Based on the M-objective penalty function,an algorithm is developed to solve an optimal solution to the inequality constrained optimization problems,with its convergence proved under some conditions.Furthermore,numerical results show that the proposed algorithm has a much better convergence than the classical penalty function algorithms under big penalty parameters,and is efficient in choosing a penalty parameter in a large range in Matlab software.展开更多
By handling the travel cost function artfully, the authors formulate the transportation mixed network design problem （MNDP） as a mixed-integer, nonlinear bilevel programming problem, in which the lower-level problem...By handling the travel cost function artfully, the authors formulate the transportation mixed network design problem （MNDP） as a mixed-integer, nonlinear bilevel programming problem, in which the lower-level problem, comparing with that of conventional bilevel DNDP models, is not a side constrained user equilibrium assignment problem, but a standard user equilibrium assignment problem. Then, the bilevel programming model for MNDP is reformulated as a continuous version of bilevel programming problem by the continuation method. By virtue of the optimal-value function, the lower-level assignment problem can be expressed as a nonlinear equality constraint. Therefore, the bilevel programming model for MNDP can be transformed into an equivalent single-level optimization problem. By exploring the inherent nature of the MNDP, the optimal-value function for the lower- level equilibrium assignment problem is proved to be continuously differentiable and its functional value and gradient can be obtained efficiently. Thus, a continuously differentiable but still nonconvex optimization formulation of the MNDP is created, and then a locally convergent algorithm is proposed by applying penalty function method. The inner loop of solving the subproblem is mainly to implement an Ml-or-nothing assignment. Finally, a small-scale transportation network and a large-scale network are presented to verify the proposed model and algorithm.展开更多
基金Project(JSPS.KAKENHI22560451) supported by the Japan Society for the Promotion of ScienceProject(69904003) supported by the National Natural Science Foundation of ChinaProject(YJ0267016) supported by the Advanced Ordnance Research Supporting Fund of China
文摘Let P（s, δ） be a sphere plant family described by the transfer function set where the coefficients of the denominator and numerator polynomials are affine in a real uncertain parameter vector δ satisfying the Euclidean norm constraint ｜｜δ｜｜〈δ. The concept of stabilizability radius of P（s, δ） is introduced which is the norm bound δs for δ such that every member plant of P（s, δ） is stabilizable if and only if ｜｜δ｜｜〈δs. The stabilizability radius can be simply interpreted as the ＇largest sphere＇ around the nominal plant P（s,θ） such that P（s, δ） is stabilizable. The numerical method and the analytical method are presented to solve the stabilizability radius calculation problem of the sphere plants.
基金Projects(11372055,11302033)supported by the National Natural Science Foundation of ChinaProject supported by the Huxiang Scholar Foundation from Changsha University of Science and Technology,ChinaProject(2012KFJJ02)supported by the Key Labortory of Lightweight and Reliability Technology for Engineering Velicle,Education Department of Hunan Province,China
文摘A methodology for topology optimization based on element independent nodal density(EIND) is developed.Nodal densities are implemented as the design variables and interpolated onto element space to determine the density of any point with Shepard interpolation function.The influence of the diameter of interpolation is discussed which shows good robustness.The new approach is demonstrated on the minimum volume problem subjected to a displacement constraint.The rational approximation for material properties(RAMP) method and a dual programming optimization algorithm are used to penalize the intermediate density point to achieve nearly 0-1 solutions.Solutions are shown to meet stability,mesh dependence or non-checkerboard patterns of topology optimization without additional constraints.Finally,the computational efficiency is greatly improved by multithread parallel computing with OpenMP.
文摘The recently improved finite order BFT Hamiltonian embedding method is applied to the two dimensional chiral bosons in non-commutative space. It is then systematically converted to a first class constraint model. Performing the momentum integrations, the corresponding fully gauge symmetry Lagrangian as well as its partition function in phase space are obtained.
基金supported by the National Natural Science Foundation of China under Grant No.11271329
文摘Some classical penalty function algorithms may not always be convergent under big penalty parameters in Matlab software,which makes them impossible to find out an optimal solution to constrained optimization problems.In this paper,a novel penalty function(called M-objective penalty function) with one penalty parameter added to both objective and constrained functions of inequality constrained optimization problems is proposed.Based on the M-objective penalty function,an algorithm is developed to solve an optimal solution to the inequality constrained optimization problems,with its convergence proved under some conditions.Furthermore,numerical results show that the proposed algorithm has a much better convergence than the classical penalty function algorithms under big penalty parameters,and is efficient in choosing a penalty parameter in a large range in Matlab software.
基金supported by the National Basic Research Program of China under Grant No. 2006CB705500the National Natural Science Foundation of China under Grant No. 0631001+1 种基金the Program for Changjiang Scholars and Innovative Research Team in University Volvo Research and Educational Foundations
文摘By handling the travel cost function artfully, the authors formulate the transportation mixed network design problem （MNDP） as a mixed-integer, nonlinear bilevel programming problem, in which the lower-level problem, comparing with that of conventional bilevel DNDP models, is not a side constrained user equilibrium assignment problem, but a standard user equilibrium assignment problem. Then, the bilevel programming model for MNDP is reformulated as a continuous version of bilevel programming problem by the continuation method. By virtue of the optimal-value function, the lower-level assignment problem can be expressed as a nonlinear equality constraint. Therefore, the bilevel programming model for MNDP can be transformed into an equivalent single-level optimization problem. By exploring the inherent nature of the MNDP, the optimal-value function for the lower- level equilibrium assignment problem is proved to be continuously differentiable and its functional value and gradient can be obtained efficiently. Thus, a continuously differentiable but still nonconvex optimization formulation of the MNDP is created, and then a locally convergent algorithm is proposed by applying penalty function method. The inner loop of solving the subproblem is mainly to implement an Ml-or-nothing assignment. Finally, a small-scale transportation network and a large-scale network are presented to verify the proposed model and algorithm.
