04066648

j

04066648 Doup, T.M. Talman, A.J.J. A continuous deformation algorithm on the product space of unit simplices. Math. Oper. Res. 12, 485-521 (1987). 1987 INFORMS, Hanover, MD EN simplicial subdivision continuous deformation algorithm V- triangulation variable dimension algorithm approximating simplex

doi:10.1287/moor.12.3.485

Summary: A continuous deformation algorithm is introduced on $S\times [1,\infty)$, where S denotes the product space of unit simplices, with arbitrary grid refinement between two subsequent levels. The set $S\times [1,\infty)$ is triangulated in such a way that for each m, $m=1,2,...,S\times \{m\}$ is triangulated by the so-called V-triangulation. The algorithm starts by applying a variable dimension algorithm on S until an approximating simplex has been found on level 1. Then the algorithm follows a path of approximating simplices in $S\times [1,\infty)$, starting on level 1, until a certain level or a certain accuracy of a solution of the underlying problem has been reached. If the algorithm returns to level 1, then we again apply the variable dimension algorithm until a new approximating simplex is found on level 1, etc. We allow solutions to lie on the boundary of $S\times [1,\infty)$ in which case the algorithm, in general, will follow a path on the boundary of $S\times [1,\infty)$.