Homotopy method for a class of nonconvex Brouwer fixed-point problems

DOI10.1016/0096-3003(95)00089-5zbMath0840.65038OpenAlexW2020041594MaRDI QIDQ1908258

Zhenghua Lin, Bo Yu

Publication date: 30 June 1996

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0096-3003(95)00089-5

zbMATH Keywords

Sard's theoremhomotopy methodsglobal Newton homotopynonconvex Brouwer fixed point problemsnormal cone condition

Mathematics Subject Classification ID

Numerical computation of solutions to systems of equations (65H10) Fixed-point and coincidence theorems (topological aspects) (54H25) Global methods, including homotopy approaches to the numerical solution of nonlinear equations (65H20) Homotopy theory (55P99) Fixed points and coincidences in algebraic topology (55M20)

Related Items (19)

Fixed point theorem: variants, affine context and some consequences ⋮ A boundary perturbation interior point homotopy method for solving fixed point problems ⋮ A noninterior path following algorithm for solving a class of multiobjective programming problems ⋮ Strong convergence on the aggregate constraint-shifting homotopy method for solving general nonconvex programming ⋮ Solving nonlinear complementarity problem by a smoothing homotopy method ⋮ 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 ⋮ Homotopy method for solving variational inequalities with bounded box constraints ⋮ Modified homotopy methods to solve fixed points of self-mapping in a broader class of nonconvex sets ⋮ 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 ⋮ Homotopy methods for solving variational inequalities in unbounded sets ⋮ The aggregate constraint homotopy method for nonconvex nonlinear programming ⋮ A smoothing homotopy method for solving variational inequalities ⋮ Generalizations of fixed point theorems and computation ⋮ Some inequality techniques in handling fixed point problems on unbounded sets via homotopy methods ⋮ Globally convergent method for designing twice spline contractual function ⋮ A continuation method for solving fixed points of self-mappings in general nonconvex sets ⋮ An infeasible homotopy method for solving fixed point problems on a general unbounded set

Cites Work

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• A Constructive Proof of the Brouwer Fixed-Point Theorem and Computational Results
• Finding Zeroes of Maps: Homotopy Methods That are Constructive With Probability One
• An exact sequence in differential topology

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