Study of Strata of Degenerate Polyhedral Cones

Project: Research

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LetAbe anm×nreal matrix. A basic problem in optimization is to decide whether a system of the formAy³0 has a solutionyÎIRndifferent from 0. That is, whether the cone of solutions is non-trivial. Iterative algorithms solving this problem when given input to the matrix A perform a number of operations, which is a function of the geometry of the cone of solutions. Intuitively, in case the cone is non-empty, the smaller it is the more difficult is to establish non-emptyness. Therefore, the analysis of the algorithms mentioned above can be done (and often is done) in terms of the geometry of the cone of solutions, which is usually captured in a number. In case this cone has full dimension (i.e., dimension n) or is trivial (reduced to the origin of coordinates) this dependency is well understood. But when the cone is degenerate (i.e., its dimension is strictly between 0 and n) it is much less so. The goal of this project is to fill this gap.


Project number9041197
Grant typeGRF
Effective start/end date1/09/0718/10/10