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1.
The Budget Constrained Multi-Product Newsboy Problem with Reactive Production: A Problem from Entrepreneurial Network Construction 下载免费PDF全文
Wenjin Li & Yanni Pang 《数学研究通讯:英文版》2012,28(2):97-107
This paper develops an extended newsboy model and presents a formulation for this model. This new model has solved the budget contained multi-product
newsboy problem with the reactive production. This model can be used to describe
the status of entrepreneurial network construction. We use the Lagrange multiplier
procedure to deal with our problem, but it is too complicated to get the exact solution. So we introduce the homotopy method to deal with it. We give the flow chart
to describe how to get the solution via the homotopy method. We also illustrate our
model in both the classical procedure and the homotopy method. Comparing the two
methods, we can see that the homotopy method is more exact and efficient. 相似文献
2.
Alfonso Reinoza 《Mathematical Programming》1985,31(3):307-320
Global Newton methods for computing solutions of nonlinear systems of equations have recently received a great deal of attention.
By using the theory of generalized equations, a homotopy method is proposed to solve problems arising in complementarity and
mathematical programming, as well as in variational inequalities. We introduce the concepts of generalized homotopies and
regular values, characterize the solution sets of such generalized homotopies and prove, under boundary conditions similar
to Smale’s [10], the existence of a homotopy path which contains an odd number of solutions to the problem. We related our
homotopy path to the Newton method for generalized equations developed by Josephy [3]. An interpretation of our results for
the nonlinear programming problem will be given. 相似文献
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Alev Kelleci Ahmet Yıldırım 《Numerical Methods for Partial Differential Equations》2011,27(4):982-995
In this study, we combined homotopy perturbation and Pade techniques for solving homogeneous and inhomogeneous two‐dimensional parabolic equation. Also, we apply our combined method for coupled Burgers' equations. The numerical results demonstrate that our combined method gives the approximate solution with faster convergence rate and higher accuracy than using the classic homotopy perturbation method. © 2010 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 27: 982–995, 2011 相似文献
5.
The main aim of the present work is to propose a new and simple algorithm for space-fractional telegraph equation, namely new fractional homotopy analysis transform method (HATM). The fractional homotopy analysis transform method is an innovative adjustment in Laplace transform algorithm (LTA) and makes the calculation much simpler. The proposed technique solves the nonlinear problems without using Adomian polynomials and He’s polynomials which can be considered as a clear advantage of this new algorithm over decomposition and the homotopy perturbation transform method (HPTM). The beauty of the paper is error analysis which shows that our solution obtained by proposed method converges very rapidly to the known exact solution. The numerical solutions obtained by proposed method indicate that the approach is easy to implement and computationally very attractive. Finally, several numerical examples are given to illustrate the accuracy and stability of this method. 相似文献
6.
Bernhard Keller 《Algebras and Representation Theory》2000,3(4):357-376
We present a new and explicit method for lifting a tilting complex to a bimodule complex. The key ingredient of our method is the notion of a strong homotopy action in the sense of Stasheff. 相似文献
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Homotopy methods are globally convergent under weak conditions and robust; however, the efficiency of a homotopy method is closely related with the construction of the homotopy map and the path tracing algorithm. Different homotopies may behave very different in performance even though they are all theoretically convergent. In this paper, a spline smoothing homotopy method for nonconvex nonlinear programming is developed using cubic spline to smooth the max function of the constraints of nonlinear programming. Some properties of spline smoothing function are discussed and the global convergence of spline smoothing homotopy under the weak normal cone condition is proven. The spline smoothing technique uses a smooth constraint instead of m constraints and acts also as an active set technique. So the spline smoothing homotopy method is more efficient than previous homotopy methods like combined homotopy interior point method, aggregate constraint homotopy method and other probability one homotopy methods. Numerical tests with the comparisons to some other methods show that the new method is very efficient for nonlinear programming with large number of complicated constraints. 相似文献
9.
An analytic technique, the homotopy analysis method (HAM), is applied to solve the generalized Benjamin–Bona–Mahony (BBM)
equation. An explicit series solution is given, different from traditional analytic techniques, our approach is independent
of knowing some parameters. This analytic method provides us with a new way to obtain series solutions of such problems. The
homotopy analysis method contains the auxiliary parameter ħ, which provides us with a simple way to adjust and control the convergence region of series solution. 相似文献
10.
Prashant Batra 《Mathematics in Computer Science》2010,4(4):507-537
Homotopy methods are of great importance for the solution of systems of equations. It is a major problemto ensure well-defined iterations along the homotopy path. Many investigations have considered the complexityof path-following methods depending on the unknown distance of some given path to the variety of ill-posed problems.It is shown here that there exists a construction method for safe paths for a single algebraic equation. A safepath may be effectively determined with bounded effort. Special perturbation estimates for the zeros together withconvergence conditions for Newton’s method in simultaneous mode allow our method to proceed on the safe path.This yields the first globally convergent, never-failing, uniformly iterative path-following algorithm. The maximumnumber of homotopy steps in our algorithm reaches a theoretical bound forecast by Shub and Smale i.e., the numberof steps is at most quadratic in the condition number. A constructive proof of the fundamental theorem of algebrameeting demands by Gauß, Kronecker and Weierstraß is a consequence of our algorithm. 相似文献
11.
In this article we extend Hilton's projective homotopy theory of modules (Hilton, 1967) to a homotopy theory of crossed modules, and then reduce some resulting homotopy classification problems to problems in group homology. We also observe that our homotopy theory satisfies the axioms of a Baues fibration category (Baues, 1989).This author would like to thank the University of Cape Town for its hospitality. 相似文献
12.
大范围求解非线性方程组的指数同伦法 总被引:1,自引:0,他引:1
为了解决关于奇异的非线性方程组求根问题,提出了一种由同伦算法推出大范围收敛的连续型方法-指数同伦法,构造了一类指数同伦方程,克服了Jacobi矩阵的奇异,分析了指数同伦方 相似文献
13.
The results of a previous paper on the equivariant homotopy theory of crossed complexes are generalised from the case of a discrete group to general topological groups. The principal new ingredient necessary for this is an analysis of homotopy coherence theory for crossed complexes, using detailed results on the appropriate Eilenberg–Zilber theory, and of its relation to simplicial homotopy coherence. Again, our results give information not just on the homotopy classification of certain equivariant maps, but also on the weak equivariant homotopy type of the corresponding equivariant function spaces. 相似文献
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Zhong-Hua Yang 《计算数学(英文版)》1991,9(2):149-154
To overcome the difficulty caused by the singularity at the pitchfork bifurcation points, we introduce the homotopy parameter so that the problem of computing the pitchfork bifurcation points can be transferred to that of computing the fold points of degree 3 with respect to the homotopy parameter. An extended system for pitchfork bifurcation points is given. The regularity of the extended system is proved. Finally, the numerical examples show the effectiveness of our method. 相似文献
16.
In this paper, homotopy perturbation transform method and modified homotopy analysis method have been applied to obtain the approximate solutions of the time fractional coupled Klein–Gordon–Zakharov equations. We consider fractional coupled Klein–Gordon–Zakharov equation with appropriate initial values using homotopy perturbation transform method and modified homotopy analysis method. Here we obtain the solution of fractional coupled Klein–Gordon–Zakharov equation, which is obtained by replacing the time derivatives with a fractional derivatives of order α ∈ (1, 2], β ∈ (1, 2]. Through error analysis and numerical simulation, we have compared approximate solutions obtained by two present methods homotopy perturbation transform method and modified homotopy analysis method. The fractional derivatives here are described in Caputo sense. 相似文献
17.
In this paper, we present a new homotopy method which is a non-interior point homotopy method for solving semi-infinite programming problems. Under suitable assumptions, we prove that the method determines a smooth path from a given point. The new homotopy method generalizes the existing combined homotopy interior point method for semi-infinite programming problems to unbounded set, moreover, it is more convenient in that it enlarges the choice scope of the initial point. Some numerical examples are given to show its efficiency. 相似文献
18.
Homotopy algorithm for symmetric eigenvalue problems 总被引:1,自引:0,他引:1
Summary The homotopy method can be used to solve eigenvalue-eigenvector problems. The purpose of this paper is to report the numerical experience of the homotopy method of computing eigenpairs for real symmetric tridiagonal matrices together with a couple of new theoretical results. In practice, it is rerely of any interest to compute all the eigenvalues. The homotopy method, having the order preserving property, can provide any specific eigenvalue without calculating any other eigenvalues. Besides this advantage, we note that the homotopy algorithm is to a large degree a parallel algorithm. Numerical experimentation shows that the homotopy method can be very efficient especially for graded matrices.Research was supported in part by NSF under Grant DMS-8701349 相似文献
19.
《Optimization》2012,61(4):585-600
In this article, a constraint shifting homotopy method (CSHM) is proposed for solving non-linear programming with both equality and inequality constraints. A new homotopy is constructed, and existence and global convergence of a homotopy path determined by it are proven. All problems that can be solved by the combined homotopy interior point method (CHIPM) can also be solved by the proposed method. In contrast to the combined homotopy infeasible interior point method (CHIIPM), it needs a weaker regularity condition. And the starting point in the proposed method is not necessarily a feasible point or an interior point, so it is more convenient to be implemented than CHIPM and CHIIPM. Numerical results show that the proposed algorithm is feasible and effective. 相似文献
20.
As a preliminary attempt for the study on nonlinear vibrations of a finite crystal plate, the thickness-shear mode of an infinite
and isotropic plate is investigated. By including nonlinear constitutive relations and strain components, we have established
nonlinear equations of thickness-shear vibrations. Through further assuming the mode shape of linear vibrations, we utilized
the standard Galerkin approximation to obtain a nonlinear ordinary differential equation depending only on time. We solved
this nonlinear equation and obtained its amplitude–frequency relation by the homotopy analysis method (HAM). The accuracy
of the present results is shown by comparison between our results and the perturbation method. Numerical results show that
the homotopy analysis solutions can be adjusted to improve the accuracy. These equations and results are useful in verifying
the available methods and improving our further solution strategy for the coupled nonlinear vibrations of finite piezoelectric
plates. 相似文献