The Sherman-Morrison Formula for the Determinant and its Application for Optimizing Quadratic Functions on Condition Sets Given by Extreme Generators

  • Gerzson Kéri
Part of the Applied Optimization book series (APOP, volume 59)


First a short survey is made of formulas, which deal with either the inverse, or the determinant of perturbed matrices, when a given matrix is modified with a scalar multiple of a dyad or a finite sum of dyads. By applying these formulas, an algorithmic solution will be developed for optimizing general (i. e. nonconcave, nonconvex) quadratic functions on condition sets given by extreme generators. (In other words: the condition set is given by its internal representation.) The main idea of our algorithm is testing copositivity of parametral matrices.


copositive matrix determinant calculus extreme generator matrix inversion matrix perturbation optimization parametral matrix quadratic programming 


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Copyright information

© Kluwer Academic Publishers 2001

Authors and Affiliations

  • Gerzson Kéri
    • 1
  1. 1.Computer and Automation Research InstituteHungarian Academy of SciencesHungary

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