This paper gives a brief list of commonly used direct and indirect efficient methods for the numerical solution of optimal control problems. To improve the low accuracy of the direct methods and to increase the convergence areas of the indirect methods we suggest a hybrid approach. For this a special direct collocation method is presented. In a hybrid approach this direct method can be used in combination with multiple shooting. Numerical examples illustrate the direct method and the hybrid approach. 相似文献
In this paper we introduce the sign matrix of a nonlinear system of equations x = Gx to characterize its hybrid and asynchronous monotonicity as well as convexity. Based on the configuration of the matrix, we define a new type of regular splittings of the system with which the solvability and construction of solutions for the system are transformed to those of the couple systems of the splitting formIt is shown that this couple systems is a general model for developing monotonic enclosure methods of solutions for various types of nonlinear system of equations. 相似文献
The algorithm described here is a variation on Karmarkar’s algorithm for linear programming. It has several advantages over
Karmarkar’s original algorithm. In the first place, it applies to the standard form of a linear programming problem and produces
a monotone decreasing sequence of values of the objective function. The minimum value of the objective function does not have
to be known in advance. Secondly, in the absence of degeneracy, the algorithm converges to an optimal basic feasible solution
with the nonbasic variables converging monotonically to zero. This makes it possible to identify an optimal basis before the
algorithm converges. 相似文献
Most mathematical models of physician decision processes offered to date, especially those relative to diagnosis and patient treatment, suffer from the inability to incorporate all useful data on the patient. Pertinent information so neglected or poorly modelled relate to variables that are intrinsically fuzzy but which describe the patient's health status. We present mathematical models based on fuzzy set theory for physician aided evaluation of a complete representation of information emanating from the initial interview including patient past history, present symptoms, signs observed upon physical examination, and results of clinical and diagnostic tests. 相似文献
Let X1,..., Xn be independent random variables such that {Xj 1}=1 and EXj=0 for all j. We prove an upper bound for the tail probabilities of the sum Mn=X1+...+ Xn. Namely, we prove the inequality {Mnx} 3.7 {Sn x}, where Sn=1+...+ n is a sum of centered independent identically distributed Bernoulli random variables such that ESn2
=MEMn2
and {k=1}=ESn2
/(n+ESn2
) for all k (we call a random variable Bernoulli if it assumes at most two values). The inequality holds for x at which the survival function x{Snx} has a jump down. For remaining x, the inequality still holds provided that we interpolate the function between the adjacent jump points linearly or log-linearly. If necessary, in order to estimate {Snx} one can use special bounds for binomial probabilities. Up to the factor at most 2.375, the inequality is final. The inequality improves the classical Bernstein, Prokhorov, Bennett, Hoeffding, Talagrand, and other bounds. 相似文献
Splitting extrapolation for solving second order elliptic systems with curved boundary in
by using isoparametric d-quadratic element Q2 is presented, which is a new technique for solving large scale scientific and engineering problems in parallel. By means of domain decomposition, a large scale multidimensional problem with curved boundary is turned into many discrete problems involving several grid parameters. The multivariate asymptotic expansions of isoparametric d-quadratic Q2 finite element errors with respect to independent grid parameters are proved for second order elliptic systems. Therefore after solving smaller problems with similar sizes in parallel, a global fine grid approximation with higher accuracy is computed by the splitting extrapolation method. 相似文献
A theorem of Ferenc Lukács states that if a periodic function
is integrable in Lebesgue"s sense and has a discontinuity of first kind at some point
, then the
th partial sum of the conjugate series to its trigonometric Fourier series at
divided by
converges to
as
. An analogue of this theorem for Walsh–Fourier series was proved by Rafat Riad. The main aim of the present paper is to extend the latter result from single to double Wals–Fourier series. We consider also functions of two variables which are of bounded variation over a rectangle in the sense of Hardy and Krause. Among others, we present a proof of the existence of the so-called sector limits of such functions at each point. 相似文献
We provide precise bounds for tail probabilities, say {Mn x}, of sums Mn of bounded i.i.d. random variables. The bounds are expressed through tail probabilities of sums of i.i.d. Bernoulli random variables. In other words, we show that the tails are sub-Bernoullian. Sub-Bernoullian tails are dominated by Gaussian tails. Possible extensions of the methods are discussed. 相似文献
We consider the linear heat equation on the half-line with a Dirichlet boundary control. We analyze the null-controllability problem. More precisely, we study the class of initial data that may be driven to zero in finite time by means of an appropriate choice of the boundary control. We rewrite the system on the similarity variables that are a common tool when analyzing asymptotic problems. Next, the control problem is reduced to a moment problem which turns out to be critical since it concerns the family of real exponentials in which the usual summability condition on the inverses of the eigenvalues does not hold. Roughly speaking, we prove that controllable data have Fourier coefficients that grow exponentially for large frequencies. This result is in contrast with the existing ones for bounded domains that guarantee that every initial datum belonging to a Sobolev space of negative order may be driven to zero in an arbitrarily small time.