Algorithm 652, HOMPACK: A suite of codes for globally convergent homotopy algorithms. There are algorithms for finding zeros or fixed points of nonlinear systems of equations that are globally convergent for almost all starting points, i.e., with probability one. The essence of all such algorithms is the construction of an appropriate homotopy map and then tracking some smooth curve in the zero set of this homotopy map. HOMPACK provides three qualitatively different algorithms for tracking the homotopy zero curve: ordinary differential equation-based, normal flow, and augmented Jacobian matrix. Separate routines are also provided for dense and sparse Jacobian matrices. A high-level driver is included for the special case of polynomial systems. (Source: http://plato.asu.edu)

References in zbMATH (referenced in 122 articles , 1 standard article )

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  1. Andò, Alessia; Breda, Dimitri; Scarabel, Francesca: Numerical continuation and delay equations: a novel approach for complex models of structured populations (2020)
  2. Hao, Wenrui; Zheng, Chunyue: An adaptive homotopy method for computing bifurcations of nonlinear parametric systems (2020)
  3. Zhu, Zhichuan; Yao, Yonghong; Postolache, Mihai: Globally convergent method for designing twice spline contractual function (2019)
  4. Easterling, David R.; Watson, Layne T.; Ramakrishnan, Naren: Probability-one homotopy methods for constrained clustering (2018)
  5. Zhu, Zhichuan; Yu, Bo: A modified homotopy method for solving the principal-agent bilevel programming problem (2018)
  6. Chen, Tianran; Lee, Tsung-Lin; Li, Tien-Yien: Mixed cell computation in HOM4ps (2017)
  7. Torres-Muñoz, Delia; Hernandez-Martinez, Luis; Vázquez-Leal, Héctor: Spherical continuation algorithm with spheres of variable radius to trace homotopy curves (2016)
  8. Yang, Li; Yu, Bo; Li, Yanxi: A homotopy method for nonlinear second-order cone programming (2015)
  9. Chen, Tianran; Lee, Tsung-Lin; Li, Tien-Yien: Hom4PS-3: a parallel numerical solver for systems of polynomial equations based on polyhedral homotopy continuation methods (2014)
  10. Torres-Muñoz, D.; Vazquez-Leal, H.; Hernandez-Martinez, L.; Sarmiento-Reyes, A.: Improved spherical continuation algorithm with application to the double-bounded homotopy (DBH) (2014)
  11. Vazquez-Leal, Hector: Piece-wise-polynomial method (2014)
  12. Zhu, Zhichuan; Yu, Bo; Yang, Li: Globally convergent homotopy method for designing piecewise linear deterministic contractual function (2014)
  13. Vazquez-Leal, H.; Marin-Hernandez, A.; Khan, Y.; Yıldırım, A.; Filobello-Nino, U.; Castaneda-Sheissa, R.; Jimenez-Fernandez, V. M.: Exploring collision-free path planning by using homotopy continuation methods (2013)
  14. Zhu, Zhichuan; Yu, Bo; Shang, Yufeng: A modified homotopy method for solving nonconvex fixed points problems (2013)
  15. Cardone, Angelamaria; Jackiewicz, Zdzislaw; Mittelmann, Hans: Optimization-based search for Nordsieck methods of high order with quadratic stability polynomials (2012)
  16. Charpentier, I.: On higher-order differentiation in nonlinear mechanics (2012)
  17. Yang, Ai-Li; Wu, Yu-Jiang: Newton-MHSS methods for solving systems of nonlinear equations with complex symmetric Jacobian matrices (2012)
  18. Yang, Fenlin; Chen, Ke; Yu, Bo: Efficient homotopy solution and a convex combination of ROF and LLT models for image restoration (2012)
  19. Yang, Fenlin; Chen, Ke; Yu, Bo: Homotopy method for a mean curvature-based denoising model (2012)
  20. Fan, Xiaona; Yan, Qinglun: Homotopy method for solving ball-constrained variational inequalities (2011)

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