Geodesic
Equation with residuated functions
Commentationes Mathematicae Universitatis Carolinae, Tome 42 (2001) no. 4, pp. 729-740.

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The structure of solution-sets for the equation $F(x)=G(y)$ is discussed, where $F,G$ are given residuated functions mapping between partially-ordered sets. An algorithm is proposed which produces a solution in the event of finite termination: this solution is maximal relative to initial trial values of $x,y$. Properties are defined which are sufficient for finite termination. The particular case of max-based linear algebra is discussed, with application to the synchronisation problem for discrete-event systems; here, if data are rational, finite termination is assured. Numerical examples are given. For more general residuated real functions, lower semicontinuity is sufficient for convergence to a solution, if one exists.
Classification : 47H05, 47J05, 90C27, 93C65
Keywords: systems of nonlinear equations; residuation theory; max-algebras 
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     title = {Equation with residuated functions},
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Cuninghame-Green, R. A.; Zimmermann, K. Equation with residuated functions. Commentationes Mathematicae Universitatis Carolinae, Tome 42 (2001) no. 4, pp. 729-740. http://geodesic.mathdoc.fr/item/CMUC_2001__42_4_a12/