S. N. Chow, J. Mallet-Paret and J. A. Yorke, Finding zeros of maps: Homotopy methods that are constructive with probability one, Math. Comp., 32(1978), 887-899. Home/Search Document Not in Database Summary Related Articles Check |
This paper is cited in the following contexts:
On Modifications of the Standard Embedding in Nonlinear.. - Noubiap (1997) (1 citation) (Correct)
....problems (regular problems in the sense of Jongen, Jonker and Twilt) cf. Definition 2:4) For the analysis with respect to JJT regular problems, we will assume a higher degree of differentiability of the problemfunctions. Let us recall now the well known concept of embedding (cf. e.g. 1] [2], 4] 9] 10] 11] 13] 21] 22] 24] Construct a one parametric optimization problem P (t) minff(y; t)jy 2 M (t)g; t 2 [0; 1] where M(t) fy 2 IR n jh i (y; t) 0; i 2 I; g j (y; t) 0; j 2 Jg n n, J is a finite index set with J J , with at least the ....
Chow, S.-N, Mallet-Paret,J. and Yorke, J.A., Finding zeros of maps: homotopy methods that are constructive with probability one, Math. Comp. 32 (1978), 887-899
A Probability-One Homotopy Algorithm For Nonsmooth Equations.. - Billups, Watson (Correct)
....This remains the topic of future work. 6. Conclusions. This paper described a probability one homotopy algorithm for solving nonsmooth systems of equations and complementarity problems. These methods are an extension to nonsmooth equations of the probability one homotopy methods described in [8, 21, 23, 24] and they are attractive because they are able to solve a qualitatively di erent class of problems than methods relying on merit functions. This claim is justi ed both theoretically and computationally. The key to success of the method is the global monotonicity assumption. When this is satis ed, ....
S.-N. Chow, J. Mallet-Paret, and J. A. Yorke, Finding zeros of maps: homotopy methods that are constructive with probability one, Mathematics of Computation, 32 (1978), pp. 887-899. 18
Continuation and Path Following - Allgower, Georg (1992) (20 citations) (Correct)
....(Id Gamma f 0 (x 0 ) x(s 0 ) s 0 ) f(x 0 ) Gamma p) and our above assumption on f implies that (Id Gamma f 0 (x 0 ) cannot have a nontrivial kernel, and hence (s 0 ) 0, i.e. the curve c is tranversal to the level = 1 at any solution. The above discussion is in the spirit of Chow, Mallet Paret and Yorke (1978). An earlier approach based on the nonretraction principle of Hirsch (1963) was given by Kellogg, Li and Yorke (1976) General discussions concerning the correspondence between degree arguments and numerical continuation algorithms have been given in Alexander and Yorke (1978) Garcia and Zangwill ....
S. N. Chow, J. Mallet-Paret and J. A. Yorke (1978), `Finding zeros of maps: Homotopy methods that are constructive with probability one', Math. Comp.
A Homotopy Based Algorithm for Mixed Complementarity Problems - Billups (1998) (Correct)
....the homotopy algorithm is embedded in a generalized Newton method. Keywords: Complementarity problems, homotopy methods, smoothing. 1 Introduction This paper discusses a robust method for solving mixed complementarity problems, which is based upon the probability one homotopy methods of [13, 31, 33]. The idea is to reformulate the mixed complementarity problem as a system of equations, and then solve smooth approximations of this system with a homotopy method. While extremely robust, the homotopy methods we have considered tend to be slower than Newton based methods. We therefore propose to ....
....criteria (7) will be satisfied by m k = 0. Thus, the inner algorithm will take full Newton steps and achieve the fast local convergence rates specified by the theorem. 2. 3 Homotopy Methods The probability one homotopy methods we consider in this paper are based on the following proposition from [13, 30, 31]: Proposition 2.10 Let F : IR n IR n be a C 2 function and suppose there exists a C 2 map ae : IR m Theta[0; 1) Theta IR n IR n such that 1. the n Theta (m 1 n) Jacobian matrix rae(a; x) has rank n on the set ae Gamma1 (0) f(a; x) j a 2 IR m ; 0 1; x 2 IR ....
S.-N. Chow, J. Mallet-Paret, and J. A. Yorke. Finding zeros of maps: homotopy methods that are constructive with probability one. Mathematics of Computation, 32:887--899, 1978.
Threading Homotopies and DC Operating Points of.. - Geoghegan, Lagarias.. (1997) (Correct)
....of Duffin [14, Theorem 3] One wants such homotopies H(x; to be bifurcation free, i.e. for the rank n condition (iii) above to be satisfied. This can be done by allowing a space of small C 2 deformations around the homotopy described above, using the approach of Chow, Mallet Paret and Yorke [7]. These homotopies certify that deg(F 0 ) 1, because deg(F 1 ) 1 by the result of Duffin [18] and the homotopy can be shown to be proper using the no gain condition. Sandwich homotopies come with no guarantee of being threading homotopies. However they have successfully been used to find more ....
S. Chow, J. Mallet-Paret and J. A. Yorke, Finding Zeros of Maps: Homotopy Methods that are Constructive with Probability One, Math. Comp. 32 (1978), 887--899.
On a Multivariate Eigenvalue Problem: - Algebraic Theory And (Correct)
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S. N. Chow, J. Mallet-Paret and J. A. Yorke, Finding zeros of maps: Homotopy methods that are constructive with probability one, Math. Comp., 32(1978), 887-899.
Relaxing Convergence Conditions To Improve The Convergence Rate - MacMillan (1999) (1 citation) (Correct)
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S. N. Chow, J. Mallet-Paret, and J. A. Yorke. Finding zeros of maps: Homotopy methods that are constructive with probability one. Mathematics of Computation, 32:887--899, 1978.
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