## Homotopy Methods and Global Convergence

Thus, the HAM provides the mathematician freedom to choose the equation-type of the high-order deformation equation and the base functions of its solution. Thus, the convergence-control parameter c 0 is a simple way to guarantee the convergence of the homotopy series solution and differentiates the HAM from other analytic approximation methods. The method overall gives a useful generalization of the concept of homotopy. The HAM is an analytic approximation method designed for the computer era with the goal of "computing with functions instead of numbers.

2. Homotopy Methods and Global Convergence.
3. Submission history.

Inspired by the recent successful applications of the HAM in different fields, a Mathematica package based on the HAM, called BVPh, has been made available online for solving nonlinear boundary-value problems . BVPh is a solver package for highly nonlinear ODEs with singularities, multiple solutions, and multipoint boundary conditions in either a finite or an infinite interval, and includes support for certain types of nonlinear PDEs. The HAM has recently been reported to be useful for obtaining analytical solutions for nonlinear frequency response equations. Such solutions are able to capture various nonlinear behaviors such as hardening-type, softening-type or mixed behaviors of the oscillator,. From Wikipedia, the free encyclopedia. Solving Frontier problems of Physics: The decomposition method.

9. Homotopy and Bifurcation

Kluwer Academic Publishers. Microsystem Technologies. Conlon, Two new conditions supporting the first-order approach to multisignal principal-agent problems,, Econometrica , 77 , Koehne, The first-order approach to moral hazard problems with hidden saving ,, Working Paper , Myerson, Optimal coordination mechanisms in generalized principal-agent problems,, J.

Prescott, Computing solutions to moral-hazard programs using the Dantzig-Wolfe decomposition algorithm,, J. Control , 28 , Su and K.

## Homotopy analysis method

Judd, Computation of moral-hazard problems ,, Working Paper , Kellogg, T. Li and J. Smale, A convergent process of price adjustment and global newton methods,, J. Chow, J. Mallet-Paret and J. Yorke, Finding zeros of maps: Homotopy methods that are constructive with probability one,, Math. Feng and B. Fujita and M.

## On a natural homotopy between linear and nonlinear single-layer networks.

Yamaguti , , 9. Feng, Z. Lin and B. Yu, Existence of an interior pathway to a Karush-Kuhn-Tucker point of a nonconvex programming problem,, Nonlinear Anal. Shang and B. Yu, Boundary moving combined homotopy method for nonconvex nonlinear programming and its convergence,, Chinese , 44 , Lin, Y. Li and B. Yu, A combined homotopy interior point method for general nonlinear programming problems,, Appl. Yang, B. Yu and Q. Xu, A constraint shifting homotopy method for general nonlinear programming ,, Optim.

Qi and Z.

Watson, S. Billups and A.

### Taiwanese Journal of Mathematics

Allgower and K. Georg, Introduction to Numerical Continuation Methods ,, 2nd edition , A new method for strong-weak linear bilevel programming problem. Yang Li , Liwei Zhang. A nonlinear Lagrangian method based on Log-Sigmoid function for nonconvex semidefinite programming. Penalty method-based equilibrium point approach for solving the linear bilevel multiobjective programming problem. A filled function method for constrained nonlinear integer programming. A structured trust region method for nonconvex programming with separable structure.

Yi Xu , Wenyu Sun. Besides, if the initial point is expanded to Rn, the global convergence of the homotopy method is ensured under a similar condition. The numerical results are reported and illustrate that the method is efficient for some nonlinear complementarity problems. More about this item Keywords Nonlinear complementarity problem ; smoothing homotopy method ; smoothing function ; global convergence ; Statistics Access and download statistics. Corrections All material on this site has been provided by the respective publishers and authors.

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