By using the BFGS correction to approximate the inverse of the Hessian matrix of the Lagrangian function, the subproblem that positive definite quadratic programming with only one linear constraint is formulated, it is always uniquely solveable and the explicit solution is obtained. Thus, the general quadratic programming or the linear equations subproblem which is usually required in the exisiting constrained nonlinear programming methods is avoided and the fast convergence property of the BFGS method is preserved.
In this Paper We Propose and demonstrate a Constrction Of magic hyper-Cubes Of the nth Order in Euclidean K dimensional Space. It is Proved thate there exists an infinite number Of the magic hgper-cubes in Euclidean K dimensional space for any positive integer K≥2. Finally, We give formulae for the representation Of all magic Cubes Of the Pth Oder, where P is an arbitrary odd integer and P≥7.
Some sufficient conditions, in terms of positive definite matrix, for stability of linear systems are given. Based on the obtained stability results, stability of second order differential systems is considered, the result proposed by [3-5] is generalized.
This paper studies some function that is expressed by means of inner product and analysis their convex. The hredominant result that followed: This kind of inner function on vector x in made of A_(n×n) which is a positive semi-definite matrix,vector α and x which are belong to n-dimension Euolidecm space. Then this kind of function is a convex function over n-dimen- sion Eulerian space.
本文研究用内积表达的某些函数,分析它们的凸性,其主要的结论如下:由一个实的半正定矩阵 An×n 及属于 n 维欧氏空间的向量 a,x 构成[x,Ax]+[a,x]+b(b 为常量)型关于向量 x 的一类内积函数,则此类函数为n 维欧氏空间上的凸函数。
Radial symmetry of positive solutions for a semilinear elliptic equation of the plolyharmonic operator involving critical exponent are proved, their explicit expressions are get and they are also the minimizers for the best constant of some Sobolev embedding theorem.