Traversing Large Pieces of Linearity in Algorithms that Solve Equations by Following Piecewise-Linear Paths

DOI10.1287/moor.5.2.242zbMath0441.90111OpenAlexW2104930957MaRDI QIDQ3883944

Michael J. Todd

Publication date: 1980

Published in: Mathematics of Operations Research (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1287/moor.5.2.242

zbMATH Keywords

fixed-point algorithmspiecewise linear homotopy algorithmspieces of linearity

Mathematics Subject Classification ID

Numerical mathematical programming methods (65K05) Numerical computation of solutions to systems of equations (65H10) Fixed-point and coincidence theorems (topological aspects) (54H25) Mathematical programming (90C99)

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A PL homotopy continuation method with the use of an odd map for the artificial level ⋮ A unified approach to the implementation of several restart fixed point algorithms and a new variable dimension algorithm ⋮ $J'$: A New Triangulation of $R^n $ ⋮ Exploiting structure in piecewise-linear homotopy algorithms for solving equations ⋮ The octahedral algorithm, a new simplicial fixed point algorithm ⋮ Computation of all solutions to a system of polynomial equations ⋮ An implementation of the simplex method for linear programming problems with variable upper bounds ⋮ Variable dimension algorithms: Basic theory, interpretations and extensions of some existing methods ⋮ On the computational complexity of piecewise-linear homotopy algorithms ⋮ An efficient simplicial algorithm for computing a zero of a convex union of smooth functions

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