Dominant eigenvalue minimization with trace preserving diagonal perturbation: Subset design problem

• Autores: Jackeline Abad Torres, Sandip Roy
• Localización: Automatica: A journal of IFAC the International Federation of Automatic Control, ISSN 0005-1098, Vol. 89, 2018, págs. 160-168
• Idioma: inglés
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• Resumen

  • Motivated by network resource allocation needs, we study the problem of minimizing the dominant eigenvalue of an essentially-nonnegative matrix with respect to a trace-preserving or fixed-trace diagonal perturbation, in the case where only a subset of the diagonal entries can be perturbed. Graph-theoretic characterizations of the optimal subset design are obtained: in particular, the design is connected to the structure of a reduced effective graph defined from the essentially-nonnegative matrix. Also, the change in the optimum is studied when additional diagonal entries are constrained to be undesignable, from both an algebraic and graph-theoretic perspective. These results are developed in part using properties of the Perron complement of nonnegative matrices, and the concept of line-sum symmetry. Some results apply to general essentially-nonnegative matrices, while others are specialized for sub-classes (e.g., diagonally-symmetrizable, or having a single node cut).