In this paper,a probe method for nonlinear programming wiht equality and inequality is given. Its iterative directions at an arbitrary point x can be obtained through solving a liear system. The terminate conditions a...In this paper,a probe method for nonlinear programming wiht equality and inequality is given. Its iterative directions at an arbitrary point x can be obtained through solving a liear system. The terminate conditions and choices of the parameters are given. The global convergence of the method is proved. Further more,some well known gradient projection type algorithms [1-15] and new gradient projection type algorithms from the linear system are given in this paper.展开更多
Study of the SISO mixed H2/l1 problem for discrete time systems showed that there exists a unique optimal solution which can be approximated within any prescribed missing error bound in l2 norm with solvable suboptima...Study of the SISO mixed H2/l1 problem for discrete time systems showed that there exists a unique optimal solution which can be approximated within any prescribed missing error bound in l2 norm with solvable suboptimal solutions and solvable superoptimal solutions.展开更多
The one-dimensional optimal system for the Lie symmetry group of the(2+1)-dimensional Wu–Zhan equation is constructed by the general and systematic approach. Based on the optimal system, the complete and inequivalent...The one-dimensional optimal system for the Lie symmetry group of the(2+1)-dimensional Wu–Zhan equation is constructed by the general and systematic approach. Based on the optimal system, the complete and inequivalent symmetry reduction systems are presented in the form of table. It is noteworthy that a new Painlev integrable equation with constant coefficient is in the table besides the classic Boussinesq equation and the steady cas of the Wu–Zhang equation.展开更多
We present a Maple computer algebra package, ONEOptimal, which can calculate one-dimensional optimal system of finite dimensional Lie algebra for nonlinear equations automatically based on Olver's theory. The core...We present a Maple computer algebra package, ONEOptimal, which can calculate one-dimensional optimal system of finite dimensional Lie algebra for nonlinear equations automatically based on Olver's theory. The core of this theory is viewing the Killing form of the Lie algebra as an invariant for the adjoint representation. Some examples are given to demonstrate the validity and efficiency of the program.展开更多
文摘In this paper,a probe method for nonlinear programming wiht equality and inequality is given. Its iterative directions at an arbitrary point x can be obtained through solving a liear system. The terminate conditions and choices of the parameters are given. The global convergence of the method is proved. Further more,some well known gradient projection type algorithms [1-15] and new gradient projection type algorithms from the linear system are given in this paper.
文摘Study of the SISO mixed H2/l1 problem for discrete time systems showed that there exists a unique optimal solution which can be approximated within any prescribed missing error bound in l2 norm with solvable suboptimal solutions and solvable superoptimal solutions.
基金Supported by the Global Change Research Program of China under Grant No.2015CB953904National Natural Science Foundation of China under Grant Nos.11375090,11275072 and 11435005+3 种基金Research Fund for the Doctoral Program of Higher Education of China under Grant No.20120076110024the Network Information Physics Calculation of Basic Research Innovation Research Group of China under Grant No.61321064Shanghai Collaborative Innovation Center of Trustworthy Software for Internet of Things under Grant No.ZF1213the Zhejiang Provincial Natural Science Foundation of China under Grant No.LY14A010005
文摘The one-dimensional optimal system for the Lie symmetry group of the(2+1)-dimensional Wu–Zhan equation is constructed by the general and systematic approach. Based on the optimal system, the complete and inequivalent symmetry reduction systems are presented in the form of table. It is noteworthy that a new Painlev integrable equation with constant coefficient is in the table besides the classic Boussinesq equation and the steady cas of the Wu–Zhang equation.
基金Supported by the National Natural Science Foundation of China under Grant Nos.11075055,11275072,61021004National High Technology Research and Development Program under Grant No.2011AA010101+1 种基金Shanghai Knowledge Service Platform for Trustworthy Internet of Things under Grant No.ZF1213Talent Fund and K.C.Wong Magna Fund in Ningbo University
文摘We present a Maple computer algebra package, ONEOptimal, which can calculate one-dimensional optimal system of finite dimensional Lie algebra for nonlinear equations automatically based on Olver's theory. The core of this theory is viewing the Killing form of the Lie algebra as an invariant for the adjoint representation. Some examples are given to demonstrate the validity and efficiency of the program.
