Optimization problem in multi-homogeneous homotopy method

DOI10.1080/10556780310001639744zbMath1064.65042OpenAlexW2112716386MaRDI QIDQ4657819

Heng Liang, Feng-Shan Bai, Xiao Yan Liu

Publication date: 14 March 2005

Published in: Optimization Methods and Software (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/10556780310001639744

zbMATH Keywords

optimizationnumerical exampleshomotopy continuation methodpartition of variablesmulti-homogeneous Bézout numberbackward greedyoptimal variable partition

Mathematics Subject Classification ID

Applications of mathematical programming (90C90) Numerical computation of solutions to systems of equations (65H10) Global methods, including homotopy approaches to the numerical solution of nonlinear equations (65H20) Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral) (30C15) Real polynomials: location of zeros (26C10)

Related Items (1)

A hybrid algorithm for multi-homogeneous Bézout number

Cites Work

• The complexity of computing the permanent
• Computing all solutions to polynomial systems using homotopy continuation
• Bézout number calculations for multi-homogeneous polynomial systems
• The number of roots of a system of equations
• Heuristic methods for computing the minimal multi-homogeneous Bézout number.
• Finding all isolated zeros of polynomial systems in \(\mathbb{C}^n\) via stable mixed volumes
• Mixed-volume computation by dynamic lifting applied to polynomial system solving
• Minimizing multi-homogeneous Bézout numbers by a local search method
• Finding all solutions to polynomial systems and other systems of equations
• Homotopies Exploiting Newton Polytopes for Solving Sparse Polynomial Systems
• Finding mixed cells in the mixed volume computation

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