Probability-one homotopies in computational science

DOI10.1016/S0377-0427(01)00473-3zbMath0996.65055MaRDI QIDQ1602815

Layne T. Watson

Publication date: 24 June 2002

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

zbMATH Keywords

convergencepolynomial systemsnonlinear equationsnonlinear constrained optimizationBrouwer fixed point problemsHOMPACK 90mathematical software packagesPOLSYS\(_-\)PLPprobability-one homotopy algorithms

Mathematics Subject Classification ID

Numerical mathematical programming methods (65K05) Numerical computation of solutions to systems of equations (65H10) Global methods, including homotopy approaches to the numerical solution of nonlinear equations (65H20) Packaged methods for numerical algorithms (65Y15)

Related Items (13)

Compact structures in a class of nonlinearly dispersive equations with time-fractional derivatives ⋮ Homotopy analysis method for limit cycle flutter of airfoils ⋮ Probability-one homotopy methods for constrained clustering ⋮ A study on the \(d\)-dimensional Schrödinger equation with a power-law nonlinearity ⋮ Solving the inverse problem of identifying an unknown source term in a parabolic equation ⋮ Optimal control and applications to aerospace: some results and challenges ⋮ Application of homotopy perturbation methods for solving systems of linear equations ⋮ Exploring collision-free path planning by using homotopy continuation methods ⋮ A TFC-based homotopy continuation algorithm with application to dynamics and control problems ⋮ A weighted algorithm based on the homotopy analysis method: application to inverse heat conduction problems ⋮ Homotopy perturbation method for a type of nonlinear coupled equations with parameters derivative ⋮ Probability-one homotopy maps for mixed complementarity problems ⋮ Application of weighted homotopy analysis method to solve an inverse source problem for wave equation

Uses Software

• HOMPACK90
• POLSYS_PLP
• HOMPACK

Cites Work

• Modern homotopy methods in optimization
• Theory of Globally Convergent Probability-One Homotopies for Nonlinear Programming
• Algorithm 652
• Numerical Linear Algebra Aspects of Globally Convergent Homotopy Methods
• Finding Zeroes of Maps: Homotopy Methods That are Constructive With Probability One
• Algorithm 777: HOMPACK90
• Algorithm 801: POLSYS_PLP
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