SEQUENTIAL QUADRATIC PROGRAMMING METHODS FOR OPTIMAL CONTROL PROBLEMS WITH STATE CONSTRAINTS

A Kind of direct methods is presented for the solution of optimal control problems with state constraints.These methods are sequential quadratic programming methods.At every iteration a quadratic programming which is obtained by quadratic approximation to Lagrangian function and Linear approximations to constraints is solved to get a search direction for a merit function.The merit function is formulated by augmenting the Lagrangian funetion with a penalty term.A line search is carried out along the search direction to determine a step length such that the merit function is decreased.The methods presented in this paper include continuous sequential quadratic programming methods and discreate sequential quadrade programming methods.     

A MODIFICATION OF POWELL-ZANGWILL'S METHOD AND ITS RATE OF CONVERGENCE

In this paper,a modified version of Powell-Zangwill's method for function minimizationwithout calculating derivatives is proposed.The new method possesses following properties:quadratic termination,global convergence for strictly convex function and Q-linearconvergence rate for uniformly convex function.Furthermore,the main part of this paperis to show that the rate of convergence of the new method is quadratic for every n(2n 1)line searches if the objective function is a uniformly convex and suitably smooth functionon R~n.     

Shape-preserving bivariate polynomial approximation inC([−1,1]×[−1,1])

In this paper we construct bivariate polynomials attached to a bivariate function, that approximate with Jackson-type rate involving a bivariate Ditzian-Totik ω2-modulus of smoothness and preserve some natural kinds of bivariate monotonicity and convexity of function.The result extends that in univariate case-of D. Leviatan in [5-6], improves that in bivariate case of the author in [3] and in some special cases, that in bivariate case of G. Anastassiou in [1].     

基于增广Lagrange函数的RQP方法

Recursive quadratic programming is a family of techniques developd by Bartholomew-Biggs and other authors for solving nonlinear programming problems.This paperdescribes a new method for constrained optimization which obtains its search di-rections from a quadratic programming subproblem based on the well-known aug-mented Lagrangian function.It avoids the penalty parameter to tend to infinity.We employ the Fletcher‘s exact penalty function as a merit function and the use of an approximate directional derivative of the function that avoids the need toevaluate the second order derivatives of the problem functions.We prove that thealgorithm possesses global and superlinear convergence properties.At the sametime, numerical results are reported.     

二元分形插值的拟合误差估计

A given bivariate continuous function is fitted by using a bivariate fractal interpolation function, and the error of fitting is studied in this paper. The results of error estimates are obtained in two metric cases. This provides a theoretical basis for the algorithms of fractal surface reconstruction.     

SHAPE-PRESERVING BIVARIATE POLYNOMIAL APPROXIMATION IN C([-1,1]×[-1,1])

In thit paper we construct bivariate polynomials attached to a btoariate function, that approximate with Jackson-type rate involving a btoariate Ditzian-Tatik ωξmodulus of smoothness and preserve some natural kinds of bivariate monotonicity and convexity of function.The result-extends that in univariate case-of D. Leviatan in [5-6], improves that in bivariate case of the author in [3] and in some special cases, that in bivariate case of G. Anastassiou in [1].     

POWER FUNCTIONS

<正>A power function of degree n is a function of the form f(x)=ax~n.For large n,it appears that the graph coincide with the x-axis near the origin,but it does not;the graph actually touches the x—axis only at the origin.     

On the Number of Limit Cycles in Small Perturbations of a Piecewise Linear Hamiltonian System with a Heteroclinic Loop

In this paper, the authors consider limit cycle bifurcations for a kind of nonsmooth polynomial differential systems by perturbing a piecewise linear Hamiltonian system with a center at the origin and a heteroclinic loop around the origin. When the degree of perturbing polynomial terms is n(n ≥ 1), it is obtained that n limit cycles can appear near the origin and the heteroclinic loop respectively by using the first Melnikov function of piecewise near-Hamiltonian systems, and that there are at most n + [(n+1)/2] limit cycles bifurcating from the periodic annulus between the center and the heteroclinic loop up to the first order in ε. Especially, for n = 1, 2, 3 and 4, a precise result on the maximal number of zeros of the first Melnikov function is derived.     

多元代数函数逼近的存在性与局部性质

The existing scheme of rational polynomial approximants, defined by multivariate power series, is extended to define approximants with branch points. The existence theorem is obtained. The basic properties used to define the rational approximants can be preserved almost intactly. Especially, the local behavior of the diagonal bivariate quadratic algebraic function approximation is analysed.     

Semi inherited bivariate interpolation

The bivariate interpolation in two dimensional space R2 is more complicated than that in one dimensional space R, because there is no Haar space of continuous functions in R2. Therefore, the bivariate interpolation has not a unique solution for a set of arbitrary distinct pairwise points. In this work, we suggest a type of basis which depends on the points such that the bivariate interpolation has the unique solution for any set of distinct pairwise points. In this case, the matrix of bivariate interpolation has the semi inherited factorization.     

The Existence and Local Behavior of Multivariate Algebraic Function Approximations

The existing scheme of rational polynomial approximants, defined by multivariate power series, is extended to define approximants with branch points. The existence theorem is obtained. The basic properties used to define the rational approximants can be preserved almost intactly. Especially, the local behavior of the     

非对角二元二次函数逼近的存在性和局部性质

§ 1　IntroductionThis paper is concerned with the properties of the simple off-diagonal bivariatequadratic Hermite-Padé approximation.Thisapproximation may be defined asfollows(see,for example,[1 ] ) .Let f(x,y) be a bivariate function,analytic in some neighbourhood of the origin(0 ,0 ) ,whose series expansion about the origin is known.Let a0 (x,y) ,a1 (x,y) ,a2 (x,y) bebivariate polynomials,a0 (x,y) = ki,j=0 a(0 )ij xiyj,a1 (x,y) = ni,j=0 a(1 )ij xiyj,a2 (x,y) = mi,j=0 a(2 )ij xiyj,such th…     

矩形网格上的二元切触有理插值

二元切触有理插值是有理插值的一个重要内容,而降低其函数的次数和解决其函数的存在性是有理插值的一个重要问题.二元切触有理插值算法的可行性大都是有条件的,且计算复杂度较大,有理函数的次数较高.利用二元Hermite（埃米特）插值基函数的方法和二元多项式插值误差性质,构造出了一种二元切触有理插值算法并将其推广到向量值情形.较之其它算法,有理插值函数的次数和计算量较低.最后通过数值实例说明该算法的可行性是无条件的,且计算量低.     

NEAR MINIMAX POLYNOMIAL APPROXIMATION

In this paper a representation for linear polynomial projection is given. Then it isshown that the near minimax approximation is equivalant to a problem of the best approxima-tion of hivariste functions. And some properties for near minimax are obtained.     

Bivariate distributions via a Pareto conditional distribution and a regression function

Uniqueness of specification of a bivariate distribution by a Pareto conditional and a consistent regression function is investigated. New characterizations of the Mardia bivariate Pareto distribution and the bivariate Pareto conditionals distribution are obtained.     

Dependent Hazards in Multivariate Survival Problems

A new class of bivariate survival distributions is constructed from a given family of survival distributions. The properties of these distributions are analyzed. It is shown that the same bivariate survival function can be derived using two radically different concepts: one involves transformation of the well-known bivariate survival function; the other involves correlated stochastic hazards. The new conditions that guarantee negative associations of life spans are derived. An exponential representation of the survival function for two related individuals is derived in terms of the conditional distribution of the stochastic hazards among survivors. Versions of the multivariate correlated gamma-frailty model are investigated.     

Bivariate segment approximation and splines

The problem to determine partitions of a given rectangle which are optimal for segment approximation (e.g., by bivariate piecewise polynomials) is investigated. We give criteria for optimal partitions and develop algorithms for computing optimal partitions of certain types. It is shown that there is a surprising relationship between various types of optimal partitions. In this way, we obtain good partitions for interpolation by tensor product spline spaces. Our numerical examples show that the methods work efficiently.     

Optimizing an objective function under a bivariate probability model

The motivation of this paper is to obtain an analytical closed form of a quadratic objective function arising from a stochastic decision process with bivariate exponential probability distribution functions that may be dependent. This method is applicable when results need to be offered in an analytical closed form without double integrals. However, the study only applies to cases where the correlation coefficient between the two variables is positive or null. A stochastic, stationary objective function, involving a single decision variable in a quadratic form is studied. We use a primitive of a bivariate exponential distribution as first expressed by Downton [Downton, F., 1970. Bivariate exponential distributions in reliability theory. Journal of Royal Statistical Society B 32, 408–417] and revisited in Iliopoulos [Iliopoulos, George., 2003. Estimation of parametric functions in Downton’s bivariate exponential distribution. Journal of statistical planning and inference 117, 169–184]. With this primitive, optimization of objective functions in Operations Research, supply chain management or any other setting involving two random variables, or calculations which involve evaluating conditional expectations of two joint random variables are direct. We believe the results can be extended to other cases where exponential bivariates are encountered in economic objective function evaluations. Computation algorithms are offered which substantially reduce computation time when solving numerical examples.     

Adaptive Bivariate Chebyshev Approximation

We propose an adaptive algorithm which extends Chebyshev series approximation to bivariate functions, on domains which are smooth transformations of a square. The method is tested on functions with different degrees of regularity and on domains with various geometries. We show also an application to the fast evaluation of linear and nonlinear bivariate integral transforms.     

二元二次对角逼近的逼近阶

给出了二元二次对角逼近的逼近阶