The Interval Analysis of Multilinear Expressions
Cosimo Laneve, Tudor A. Lascu, Vania Sordoni · Electronic Notes in Theoretical Computer Science · 2010
Expressions are multilinear when variable occurrences are linear and products have factors using different variables. We demonstrate that multilinear expressions are either constant or have never a local minimum or a local maximum. Therefore the interval of multilinear expressions may be computed precisely studying their values at the bounds of the variables therein. We then propose a technique for the interval analysis of generic expressions that transforms them into multilinear ones and computes the interval of the latters.