NP-hardness of polytope M-matrix testing and related problems
Nikos Vlassis
TL;DR
This paper proves that determining whether a convex combination of given matrices is a nonsingular M-matrix is NP-hard, impacting the computational complexity of key problems in systems analysis and control.
Contribution
It establishes NP-hardness for the M-matrix testing problem and related issues like system instability and spectral radius minimization.
Findings
NP-hardness of convex combination M-matrix testing
Implications for system stability analysis
Complexity results for spectral radius minimization
Abstract
In this note we prove NP-hardness of the following problem: Given a set of matrices, is there a convex combination of those that is a nonsingular M-matrix? Via known characterizations of M-matrices, our result establishes NP-hardness of several fundamental problems in systems analysis and control, such as testing the instability of an uncertain dynamical system, and minimizing the spectral radius of an affine matrix function.
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Taxonomy
TopicsMatrix Theory and Algorithms · Advanced Optimization Algorithms Research · graph theory and CDMA systems