Globally convergent homotopy methods: a tutorial
TLDR
Homotopy algorithms for solving nonlinear systems of (algebraic) equations, which are convergent for almost all choices of starting point, are globally convergent with probability one and exhibit a large amount of coarse grain parallelism.About:
This article is published in Applied Mathematics and Computation.The article was published on 1989-05-01 and is currently open access. It has received 123 citations till now. The article focuses on the topics: n-connected & Homotopy analysis method.read more
Citations
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More on homotopy continuation method and discounted zero-sum stochastic game with ARAT structure
A. Dutta,Apurva Kumar Das +1 more
TL;DR: In this paper , a homotopy function is introduced to trace the trajectory of a two-person zero-sum discounted stochastic ARAT game, and a modified homo-opy continuation method is applied to find the solution of the game.
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Residue-regulating homotopy method for strongly nonlinear oscillators
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On the continuation-path uniqueness of homotopy enhanced power flow method for general distribution networks with distributed generators
Hsiao-Dong Chiang,Tao Wang +1 more
TL;DR: A set of sufficiently conditions for the uniqueness of power flow solution is proposed, by showing theiqueness of continuation path in a homotopy method, which can serve as the condition for controlling when to apply the costly global-searching techniques for finding multiple power flow solutions.
Proceedings ArticleDOI
Impacts of transient instability on power system reliability
TL;DR: In this article, three probabilistic transient stability indices are proposed to assess system robustness against transient contingencies and update the reliability indices, and the results showed that the effect of transient instability should not be ignored.
Posted Content
Bounded Homotopy Path Approach to Find the Solution of Linear Complementarity Problems
TL;DR: In this article, a homotopy function based on the Karush-Kuhn-Tucker condition of the corresponding quadratic programming problem of the original linear complementarity problem is proposed.
References
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Book
Numerical Methods for Unconstrained Optimization and Nonlinear Equations (Classics in Applied Mathematics, 16)
TL;DR: In this paper, Schnabel proposed a modular system of algorithms for unconstrained minimization and nonlinear equations, based on Newton's method for solving one equation in one unknown convergence of sequences of real numbers.
Book
Numerical methods for unconstrained optimization and nonlinear equations
TL;DR: Newton's Method for Nonlinear Equations and Unconstrained Minimization and methods for solving nonlinear least-squares problems with Special Structure.
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An incremental approach to the solution of snapping and buckling problems
TL;DR: In this paper, an incremental approach to the solution of buckling and snapping problems is explored, where the authors use the length of the equilibrium path as a control parameter, together with the second order iteration method of Newton.