A continuation method for solving fixed points of self-mappings in general nonconvex sets

Lin, Zhenghua; Yu, Bo; Zhu, Daqi

doi:10.1016/s0362-546x(02)00140-2

Cited by 11 publications

(12 citation statements)

References 5 publications

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“…. ,m, which may help us to establish constructively the general Brouwer fixed point theorem on more general nonconvex sets than those in [9,12]. In this paper, under commonly used conditions in the literature, a bounded smooth homotopy path from a given point to a fixed point will be proven to exist.…”

Section: Introductionmentioning

confidence: 87%

“…This point is also important for it is difficult to construct such a homeomorphism in practice. Moreover, in [9], Lin et al generalized the results in [12] to more general nonconvex sets.…”

Section: Introductionmentioning

confidence: 99%

“…But in [9,12], initial guesses are generally confined in Ω, which is not easy to be localized for many cases, hence it is essential to enlarge the scope of choice of initial guesses. To this end, in this paper, we apply proper perturbation on the constrained functions of Ω and hence develop a boundary perturbation interior point homotopy method.…”

Section: Introductionmentioning

confidence: 99%

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A boundary perturbation interior point homotopy method for solving fixed point problems

Shi

2011

Journal of Mathematical Analysis and Applications

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In this paper, a boundary perturbation interior point homotopy method is proposed to give a constructive proof of the general Brouwer fixed point theorem and thus solve fixed point problems in a class of nonconvex sets. Compared with the previous results, by using the newly proposed method, initial points can be chosen in the whole space of R n , which may improve greatly the computational efficiency of reduced predictor-corrector algorithms resulted from that method. Some numerical examples are given to illustrate the results of this paper.

show abstract

Section: Introductionmentioning

confidence: 87%

“…This point is also important for it is difficult to construct such a homeomorphism in practice. Moreover, in [9], Lin et al generalized the results in [12] to more general nonconvex sets.…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A boundary perturbation interior point homotopy method for solving fixed point problems

Shi

2011

Journal of Mathematical Analysis and Applications

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“…The solution algorithm presented in [177] represents a slightly different approach based on a so-called homotopy method [3,115,171] and a relaxed fixed-point iteration. At first, the authors rewrote the EL equation (5.25) as…”

Section: Solution Algorithms For the Generalized Mean Curvature Modelmentioning

confidence: 99%

A New Augmented Lagrangian Approach for $L^1$-mean Curvature Image Denoising

Myllykoski¹,

Glowinski²,

Kärkkäinen³

et al. 2015

SIAM J. Imaging Sci.

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“…In 2003, Lin, Yu and Zhu [5] constructed a modified combined homotopy for computing Brouwer fixed points in nonconvex bounded sets Ω = {x : g i (x) ≤ 0, i = 1, 2, . .…”

Section: Introductionmentioning

confidence: 99%

A constraint shifting homotopy method for computing fixed points on nonconvex sets

Zhu¹,

Yang²

2016

J. Nonlinear Sci. Appl.

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In this paper, a constraint shifting homotopy method for solving fixed point problems on nonconvex sets is proposed and the existence and global convergence of the smooth homotopy pathways is proved under some mild conditions. Compared with the previous results, the newly proposed homotopy method requires that the initial point needs to be only in the shifted feasible set not necessarily in the original feasible set, which relaxes the condition that the initial point must be an interior feasible point. Some numerical examples are also given to show the feasibility and effectiveness of our method.

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A continuation method for solving fixed points of self-mappings in general nonconvex sets

Cited by 11 publications

References 5 publications

A boundary perturbation interior point homotopy method for solving fixed point problems

A boundary perturbation interior point homotopy method for solving fixed point problems

A New Augmented Lagrangian Approach for $L^1$-mean Curvature Image Denoising

A constraint shifting homotopy method for computing fixed points on nonconvex sets

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