Modified homotopy methods to solve fixed points of self-mapping in a broader class of nonconvex sets

DOI10.1016/j.apnum.2006.11.008zbMath1154.65331OpenAlexW2082707229MaRDI QIDQ2479419

Zhenxin Liu, Menglong Su

Publication date: 26 March 2008

Published in: Applied Numerical Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.apnum.2006.11.008

zbMATH Keywords

nonconvex setsunbounded convex setscombined homotopy interior point method

Mathematics Subject Classification ID

Numerical computation of solutions to systems of equations (65H10) Numerical solution of nonlinear eigenvalue and eigenvector problems (65H17)

Related Items (6)

Solving fixed-point problems with inequality and equality constraints via a non-interior point homotopy path-following method ⋮ A parameter perturbation homotopy continuation method for solving fixed point problems with both inequality and equality constraints ⋮ Existence of an interior path leading to the solution point of a class of fixed point problems ⋮ A modified infeasible homotopy algorithm for computing fixed point in general non-convex set ⋮ Some inequality techniques in handling fixed point problems on unbounded sets via homotopy methods ⋮ An infeasible homotopy method for solving fixed point problems on a general unbounded set

Cites Work

• A new polynomial-time algorithm for linear programming
• A globally convergent algorithm for computing fixed points of \(C^2\) maps
• Homotopy method for a class of nonconvex Brouwer fixed-point problems
• Tracking nonlinear equilibrium paths by a homotopy method
• An Approach to Homotopy and Degree Theory
• An Algorithm That is Globally Convergent with Probability One for a Class of Nonlinear Two-Point Boundary Value Problems
• A Constructive Proof of the Brouwer Fixed-Point Theorem and Computational Results
• Finding Zeroes of Maps: Homotopy Methods That are Constructive With Probability One
• A Constructive Proof of the Poincare-Birkhoff Theorem
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